Asked by Kelly

conic sections

prove that the line x-2y+10=0 touches the ellipse 9x^2+64y^2=576

show that the equation of the normal to the ellipse x^2/a^2 + y^2/b^2 = 1 at the point (a cos theta, b sin theta ) is ax sin theta - by cos theta - (a^2-b^2) sin theta cos theta =0

Answers

Answered by drwls
For the first part, require that
x = 2y -10 . Then insert that value of x in the second (ellipse) equation and see if a solution exists. If it does, there is a point that satisfies both equations.

Part 2, determine the slope dy/dx of the tangent line at (x = a sin theta, y = b cos theta)

2x/a^2 + (2y/b^2) dy/dx = 0
dy/dx = -(x/y)(b/a)^2
= (tan theta)(b/a)
(theta is measured counterclockwise from the +x axis)

Knowing the slope and the given coordinates (x,y) of one point on the tangent line, the equation for the tangent line can be written.
There are no AI answers yet. The ability to request AI answers is coming soon!

Related Questions