24kk
tangent at pt (t2,2t) will be
x-ty+t2=0
and normal at (√5 cosφ, 2sinφ)will be
√5secφ x -2cosecφ y-1=0
Now any method will give relation b/w them
If the tangent drawn from the point (t2,2t) on the parabola y2=4x is same as the normal drawn at a point (√5 cosφ, 2sinφ)
on the ellipse 4x2+5y2=20, Find the values of t and φ.
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8 Answers
24the question should be tangent at point (t2,2t) on the parabola y2=4x
and not on
24
62x-ty+t2=0
x -2cosecφ/√5secφ y-1/√5secφ =0
x -2/√5 cot φ y - cosφ /√5 =0
compare the coeff
t=2/√5 cot φ
t2=- cosφ /√5 = 4/5cot2 φ
hence, you can find a quadratic in cos φ
Now solve it for the -ve root.. (why -ve root?)