Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 = 0. -

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: Find the tangent to the parabola (x + 2y)² + 2x - y - 3 = 0, parallel to the line x - y = 1.

A: Consider the equation of the line x-y=1 ⇒y=x -1 Comparing with y=mx+c we get slope of line, m=1

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

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Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

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Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

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Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

Q: Find equations of both lines through the point (2, −30) that are tangent to the parabola y = x^2 -…

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Q: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.

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Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

Q: Show that the line b2xx1 + a2yy1 - a2b2 = 0 is tangent to the ellipse b2x2 + a2y2 - a2b2 = 0 at the…

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

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Q: Find the point Q that is on the curve nearest %3D the point (4, 1)

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Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: The x coordinate of the point of intersection between the two curves y = el4a and y = 1 is

A: Equate both equation

Q: Find the equation of the line segment tangent to the curve y−2x2−1=0y−2x2−1=0 which is parallel to…

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Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: Find equations of both lines through the point (2, - 3) that are tangent to the parabola y = x2  + x…

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Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x +y +5 = 0. YI…

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Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

Q: Find equations of both the tangent lines to the ellipse x2 +4y2 =36that pass through the point (12,…

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Q: The slope of the tangent line to the parabola y 3x? + 6x + 2 at the point (- 2, 2) is: The equation…

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

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Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: Find equations of both lines through the point (-2,-18) that are tangent to the parabola y = x² + 3x

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Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

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

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Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: Find equations of both the tangent lines to the ellipse x + 9y2 81 that pass through the point (27,…

A: Given information: The equation of the ellipse is x2+9y2=81. Calculation: We need to find the…

Q: (a) Where does the normal line to the ellipse x2- x   y + y 2 = 3 at the point (1, -1) intersect the…

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Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

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Q: Find the equation of the line tangent to the ellipse x^2 - xy + 2y^2 - 4x + 2y + 2 = 0 if the…

A: given equation of ellipse x2-xy+2y2-4x+2y+2=0 and a line  4y-x+2=0 to find equation of line tangent…

Q: Find the length of the curve. y = In(secx), 0Sx</4

A:

Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

A:

Q: What are the coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?

A: Given, To find coordinates of center for the curve x2 + y2 – 2x – 4y – 31 = 0?

Q: Find the equation of the line tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 =…

A:

Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

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

A: Find the slope of curve. Find the derivative of the following function.

Q: Find the tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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Q: Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A: This is a problem of geometry. We will calculate slope of x, y and z at given point and general…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.