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← JEE Main 2022 · 29 Jun · Shift 1
MathematicsSingle correct+4 / -1Question 19 of 90

JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 19

Let the tangent to the circle C1:x2+y2=2C_1:x^2+y^2=2 at the point M(−1,1)M(-1,1) intersect the circle C2:(x−3)2+(y−2)2=5C_2:(x-3)^2+(y-2)^2=5, at two distinct points A and B. If the tangents to C2C_2 at the points A and B intersect at N, then the area of the triangle ANB is equal to :

Choose one option
Answer and worked solution

Official answer: C

Tangent at M. y−x=2y-x=2. Its distance from (3,2)(3,2) is 32\frac3{\sqrt2}, so the half-chord is 5−92=12\sqrt{5-\frac92}=\frac1{\sqrt2}.

Pole N is at distance r2d=523\frac{r^2}d=\frac{5\sqrt2}3 from the centre, i.e. 132\frac1{3\sqrt2} beyond the chord.

Area. 12⋅2⋅132=16\frac12\cdot\sqrt2\cdot\frac1{3\sqrt2}=\frac16.

(C)

Topics:Chord of contactTangents and normals
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