Question
Question: If a tangent to ellipse \(\frac{x^{2}}{a^{2}}\)+ \(\frac{y^{2}}{b^{2}}\)= 1 makes an angle a with x-...
If a tangent to ellipse a2x2+ b2y2= 1 makes an angle a with x- axis, then square of length of intercept of tangent cut between axes is-
A
a2tan2a + b2 cot2a
B
a2 sec2a + b2 cosec2a
C
a2 cosec2a + b2 sec2a
D
None of these
Answer
a2 sec2a + b2 cosec2a
Explanation
Solution
Let tangent is axcosθ+bysinθ= 1
Slope is tan a = –abcot q … (1)
\ square of length of intercept is
= (a sec q)2 + (b cosec q)2
\ Length is L = a2 + b2 + a2tan2q + b2 cot2 q … (2)
Now use value of tan q from (1)