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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

h2a22ka\frac{h^{2}}{a^{2}} - 2\frac{k}{a} = 4

h2 – 2ak = 4a2

h2 = 2ak + 4a2

x2 = 2a(y + 2a)