Find equations of both lines through the point (5, –6) that are tangent to the parabola y = x2 – 3x

Q: Find the points on the curve x = t – 4t – 9, y = t2 + 14t + 4 that have: A. a horizontal tangent…

A:

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,   (−7, 49/2)

A: The objective is to find the equation of the tangent line to the parabola at the given point.

Q: Show that the equation of the tangent line to the hyperbola                        x2/a2 − y2/b2 = 1…

A: Given Data The equation of the hyperbola is x²/ a²- y²/ b²=1. The points are (x0,y0).…

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

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 an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

A:

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: Find the points on the curve a = ť² – 14t – 9, y =t² + 14t + 1 that have: | A. a horizontal tangent…

A:

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

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

A:

Q: Find the equation of the tangent plane to the surface - 8x3 + 7y³ + 3xy at the point (2,0, 64).

A:

Q: dy 20 yx %3D

A:

Q: Find the equations of the tangent lines x = t3 − 6t, y = t2 at the point where the curve crosses…

A: To find the equations of the tangent linesx=t3-6t,y=t2 at the point where the curve crosses itself.…

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

A:

Q: b) Show that the equation of the tangent line to the x², y? Xox at (xo, Yo) is Yo.y + a² ellipse 31.…

A:

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

A:

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

A:

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

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Show that the equation of the tangent to the curve = 2 (a'0, b1.0) a y at the point (a, b) is = 2.…

A:

Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Find the tangent lines as directed. To the parabola y=6x-3 perpendicular to the line x+3y=7

A:

Q: Find an equation of the tangent plane to the surface 3x? + 2xy – 4z2 + 2x – 3y = 0 at the point P(0,…

A:

Q: Find the equations of the tangent lines x = t2 − t, y = t3 − 3t − 1 at the point where the curve…

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 =…

A:

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Find the points on the curve t2 – 14t – 1, y = t² + 6t + 5 that have: х — A. a horizontal tangent…

A:

Q: Find the equation of the tangent and normal to the parabola y=4ax at the point (at²,2at)

A:

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: Show that the equation of the tangent line to the hyperbola x2/a2 − y2/b2 = 1 at (x0, y0) is x0x/a2…

A:

Q: Given the parabola: x2+12y=0 and the tangent line x+y-3=0, find the point of tangency

A:

Q: Find the tangent plane to the equation z 5x? – 2y? – 5y at the point (3, 0, 45).

A: We need to find the tangent plane equation at (3,0,45)

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

A:

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

A:

Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

A:

Q: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

A:

Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y2 + 5z2 = 177, P =…

A:

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

A:

Q: The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B. Find the…

A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…

Q: Which of the following points do not lie on any tangent line of the parabola y = x2 + 2? (2,6) O…

A:

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

A:

Q: Find an equation of the tangent plane to the surface z = y? - x² at the point (-4,5,9).

A: Finding partial derivatives with respect to x and y for finding plane equation.

Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

A:

Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

A:

Q: A parabola has an equation of x² = 6y + 10. Compute the equation of a tangent to the curve which has…

A: Given that a parabola has an equation x2=6y+10. Here we have to compute the equation of a tangent to…

Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

A:

Q: Find an equation for the tangent plane to z = 9x? – 8y² at the point (1, 1, 1). - = 0.

A: Here we find the equation of tangent plane.

Q: Find an equation of the tangent plane to the surface at the given point. xy2 + 3x – z2 = 56, (5, -3,…

A: Given:   xy2 + 3x - z2 = 56  Point ( 5 , -3, 2 )