Question

$\huge\boxed{\dag\sf\red{Question}\dag}$. → The equation of the pair of tangents drawn from the pôint (1,2) to the ellipse 3x²+2y²=5.​

Answer 1

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Answer 2

Answer:

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Tan −1

( 512 )

Equation of line through (1,2) is y−2=m(x−1)

⇒y=mx+(2−m)

Equation for tangency is c 2 =a 2 m 2+b 2

(2−m) 2 = 35m 2 + 254+m 2 −4m= 35

m 2 + 25 = 32 m 2 +4m− 23 =0 m 1 +m2 = 32

−4 =−6m -1m 2 =− 2/3−3/2 = 4−9

(m1) −m 2 ) 2 =(m 1 +m 2) 2 −4m 1 m 2

⇒m 1 −m2 −45

∴tanα= 1+m 1m 2m

1 −m

2 = 54 45 = 3×4 = 512

∴α=tan −1 ( 512 )

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