Draw a diagram to show that there are two tangent lines to the parabola y = x 2   that pass through the point (0 , - 4 ) . Find the coordinates of the points where these tangent linesintersect the parabola.

Q: Find an equation of the tangent to the circle x2+y2=36 at the point (5,3)

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

A: We have to find equations of both lines through the point (2 , -3) that are tangent to the parabola…

Q: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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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: (a) Find all the points on the graph of (x² + y? + y)2 x² + y? that have horizontal tangent line.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the Difference Quotient to evaluate the slope of the tangent line to the first parabola found in…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

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Q: Find the slope of the tangent line to the circle 4x² + 9y² = 36 at the point (0,2).

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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 lines through the point (2, –3) that are tangent to the parabola y = x2 + x.

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Q: Find the equation of the tangent plane to the surface 4 =1 at the point 9. 16 (1,-3,2)

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Q: Find an equation of the tangent plane to the given surface at the specified point. 2. (-16, 4, -1)

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Q: Find the equation of one of the tangent lines to the circle x^2 + y^2 = 5^2 that passes through the…

A: Here, to find the equation of the tangent line to the circle  x2+y2=52⇒x2+y2=25...(1) that passes…

Q: Find the slope of the tangent line to the curve -2x^2-3xy-3y^3 = -246` %3D at the point `( 3,4).…

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Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

Q: What are the coordinates of the points in the graph of y-x+6x-13=0 in which the tangent line is…

A: Given query is to find the point where tangent line is horizontal.

Q: 2. Find the equations of both the tangent lines to the parabola y through the point (3, 16). :-

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Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: On a separate piece of paper, sketch the graph of the parabola y = x² + 9. On the same graph, plot…

A: Sketch the figure.

Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: Find an equation of the tangent line to the parabola y − x2 - 8x + 9 at the point (3, -6).

A: The derivative of a curve at a point gives the slope of the tangent to the curve. It can be…

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 the equations of the tangent lines to the parabola y = -x² + 5x – 6 at its points of…

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Q: The slope of the tangent line to the parabola y 3x2 + 2x + 6 at the point (5, 91) is: The equation…

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Q: Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).

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Q: Find the equation of the tangent line to the circle at the point (-3, -4). Equation of the circle *…

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Q: The x-coordinate of the point where the tangent line to the parabola y=2x^2 at x=1 intersects the…

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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: Give the equation of the tangent which passes through the point with the coordinate x=2 of the…

A: Equation of tangent problem.....

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y? - 32? . = 82, (-7,…

A: Given equation  x2+y2−3z2=82,     (-7,-6,1)

Q: Find an equation of the tangent plane to the surface at the given point. x²+²-72²-38, (-3, -6, 1)

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Q: Find the slope of the tangent line to the parabola y= 2 +x−x^2 at the point (0,2).

A: Simply take the derivative of the given equation and substitute the given point.

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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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 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 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 equations of both lines that pass through the point (2, –3) and are tangent to the…

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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: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

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Q: Find an equation of the tangent plane to the surface at the given point. 5 —х — у, z = 5 - (3, -2,…

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Q: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: The slope of the tangent line to the parabola y=2x^2+2x+7 at the point where x=4 is: slope =…

A: The equation of the parabola is y=2x2+2x+7

Q: Find an equation of the tangent to the circle x 2 + y 2= 25 at the point  (3,4)

A: x2+y2=25 Differentiating with respect to x, we get 2x+2y·dydx=0⇒2y·dydx=-2x⇒dydx=-xy Now slope of…

Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: Find an equation of the tangent plane to the surface at the given point. + 3x – z2 = 56, (5, -3, 2)

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