Find equations for the tangent lines and the normal lines to the hyperbola for the given value of x. (The normal line at a point is perpendicular to the tangent line at the point.) = 1, x = 3 3 (a) tangent lines (smaller y-component of the two tangent points) x- yv2 -1=0 (larger y-component of the two tangent points) (b) normal lines (smaller y-component of the two tangent points) (larger y-component of the two tangent points) Need Help? Watch it Read It

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: 1. Find the equation for the parabola that has its vertex at the origin and has directrix at y = 25…

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: A hyperbola has two curves that do not touch each other.  A hyperbola is a curve whose equation is…

Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

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Q: 8. Determine the Equation of the Hyperbola if the Transverse Axis is 8 and the Foci are at (0, ±6)

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Q: A hyperbola in standard position has equation 36x2 −49y2 −100 = 0. Write down a parametrisation of…

A: The given equation of the hyperbola is: 36x2-49y2-100=0 Rewrite the equation:…

Q: Find an equation of the hyperbola that has foci at (-15, 0) and (15, 0), and asymptotes y= x and y=

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Q: center, horizontally, is the car when it is at an altituue Ul 23 IL! 2. A truck has to pass under an…

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Q: 27 4) and has directrix at Find the equation for the parabola that has its focus at the 11 equation…

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Q: 1. Find the slope and the equation of the tangent line to the curve y=x³ at x=-1 2. Find the slope…

A: Let's find.

Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: We have, a hyperbola satisfies the given conditions as vertical transverse axis of length 10,…

Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: By differentiating implicitly, find the slope of the hyperboloid x² + y? - z2 = 1 in the x-direction…

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Q: Find the equation of one of the tangents to the ellipse 2x² + 4y² = 48 with slope of mt = 1.

A: The given equation of the ellipse is, 2x2+4y2=48 To find the slope of the tangent to the ellipse, we…

Q: Determine the area of the largest circle that can be enclosed by the two hyperbolae, xy= 1 and xy =…

A: Solution is here

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

Q: Find an equation in standard form for the hyperbola that satisfies the given conditions. Transverse…

A: In a hyperbola the straight line joining two vertices is the Transverse axis Distance between the…

Q: suppose that a non periodic comet will visit the solar system with the sun located at the focus of…

A: Parabolic trajectory of comet is 16y - 24 = x2. and sun located at its focus while earth at the…

Q: Determine the equation of the tangent and normal to : 1. The parabola y² = 6x - 3 perpendicular line…

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Q: length of the latus rectum of a hyperbola is equal to 18 and the di equation of the curve if the…

A: The length of the latus rectum = 18,  The distance between the foci = 12,  We have to find the…

Q: 1. A parabola with directrix y = -1 and one endpoint of the latus rectum at (-1,3)

A: As per our guidelines we can answer only one question. please repost other seperately.  First of all…

Q: Find the equation of the hyperbola whose center is at point (4,−1), transverse axis parallel to…

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Q: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) & (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

Q: Find an equation of the hyperbola that has foci at (-10,0) and (10,0) , and asymptotes y=3x and…

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Q: Identify the type of conic section whose equation is given. 3x2 = y + 3

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Q: 1. Parabolas with axis parallel to the x-axis with focal distance “a" fixed.

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Q: Find the Differential Equation of the Family of Ellipses with its center at the origin.

A: Here is the solution:

Q: 8. Find the equation of the parabola with vertex at (0, 5) and passing through the point (4,3)…

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Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: 64. Find equations of both the tangent lines to the ellipse x² + 4y2 = 36 that pass through the…

A: Given: The Equation of the ellipse is x2 + 4y2 = 36

Q: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

A: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

Q: Which is the corresponding equation of the hyperbola with foci located at (-8, 0) and (8, 0) and a…

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Q: Find a Cartesian equation for the hyperbola centered at the origin that has a focus at (3, 0) and…

A: The focus is 3,0 c,0=3,0∴c=3 Also the directrix x=ae=1                           ∴a=e Now…

Q: Find an equation of the tangent line to the hyperbola defined by (5x^2)+(4xy)−(2y^2)−4x=195 at the…

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Q: d the standard form of the equation of the circle, if the center of the circle of radius 3 lies on…

A: Here we have to find the standard equation of the circle if the center of the circle of radius 3…

Q: Find the equation of the hyperbola with center at (-3,3); transverse axis parallel to y-axis; length…

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Q: Find the standard form equation for a hyperbola with vertices at (0, 2) and (0, – 2) and 1 asymptote…

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Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

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Q: Determine the eccentricity of a hyperbola with a horizontal transverse axis of length 24 units and…

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Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

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Q: Find the standard form equation for a hyperbola with vertices at (8, 0) and (– 8, 0) and asymptote 3…

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Q: 9. Find equations for two lines through the origin that are tangent to the ellipse 1² – 4x + 4y² =…

A: We have to find

Q: Find the standard form equation for a hyperbola with vertices at (12,0)(12,0) and (−12,0)(-12,0) and…

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Q: Suppose that two microphones 1500 m apart at points A and B detect the sound of a rifle shot. The…

A: Frist draw a diagram with given information as shown in below figure.

Q: How would this problem be solved parametrically?

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Q: 11. Show that the tangent to the hyperbola x- y = 1 at the pomt P(coshu, sinhu), cuts the x-axis at…

A: We will be using the definition of tangent line to solve the problem

Q: Find the standard form equation for a hyperbola with vertices at (6, 0) and (- 6, 0) and asymptote y…

A: The vertices of the hyperbola is:  (6, 0)  and  (-6, 0) The asymptote of the hyperbola is:  y=13x

Q: Find a Cartesian equation for the hyperbola centred at (3,0) with x=1 as one equation of the…

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