Question
Question: Tangents PA and PB are drawn to x<sup>2</sup> = 4ay, if m<sub>1</sub>& m<sub>2</sub> be the slopes o...
Tangents PA and PB are drawn to x2 = 4ay, if m1& m2 be the slopes of these tangents and m12 + m22 = 4 then locus of P is
A
x2 = 2a(y – a)
B
x2 = y(y – a)
C
x2 = 2a(y + 2a)
D
None
Answer
x2 = 2a(y + 2a)
Explanation
Solution
Equation of tangents in slope form
y = mx – am2
(h, k)
k = mh – am2
am2 – mh + k = 0
m1 + m2 = h/a
m1 m2 = k/a
m12 + m22 = 4
(m1 + m2)2 – 2m1m2 = 4
a2h2−2ak = 4
h2 – 2ak = 4a2
h2 = 2ak + 4a2
x2 = 2a(y + 2a)