@oldrin.bataku help me with the following please!
Show that the tangent to the ellipse x^2/a^2+y^2/b^2=1 at the point P(a*cos(theta),B*sin(theta)) has equation bx*cos(theta)+ay*sin(theta)=ab.
Hence do the following
(a) the tangent to the ellipse at P meets the x-axis at Q and the y-axis at R. the mid-point of QR is M Find a cartesian equation for the locus of M as a function of theta
(b) the tangent to the ellipse at P meets the line x=a at T and point A is (-a,0). Prove that OT is parallel to AP

Question

@oldrin.bataku  help me with the following please!
Show that the tangent to the ellipse x^2/a^2+y^2/b^2=1 at the point P(a*cos(theta),B*sin(theta)) has equation bx*cos(theta)+ay*sin(theta)=ab.
Hence do the following
(a) the tangent to the ellipse at P meets the x-axis at Q and the y-axis at R. the mid-point of QR is M Find a cartesian equation for the locus of M as a function of theta
(b) the tangent to the ellipse at P meets the line x=a at T and point A is (-a,0). Prove that OT is parallel to AP

amistre64 · Answer

might want to consider taking a derivative to start with

caozeyuan · Answer

yep, I've done part one successfully, but question (a) and (b) killed me!

amistre64 · Answer

use the tangent line eqution to define Q and R

(Q+R)/2 = M

algebrate thru it to solve for theta

amistre64 · Answer

you will most likely get a polar equation that youd have to eliminate a parameter if im seeing it correctly

caozeyuan · Answer

oh, that's a good solution, thanks. But how about (b), it sucks as much as (a) does

amistre64 · Answer

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can you do vectors with it?  or does it simply have to be linear equations?