Question:
Let the tangent to the circle C1: x2 + y2 = 2 at the point M(–1, 1) intersect the circle C2: (x – 3)2 + (y – 2)2 = 5, at two distinct points A and B. If the tangents to C2 at the points A and B intersect at N, then the area of the triangle ANB is equal to
Let the tangent to the circle C1: x2 + y2 = 2 at the point M(–1, 1) intersect the circle C2: (x – 3)2 + (y – 2)2 = 5, at two distinct points A and B. If the tangents to C2 at the points A and B intersect at N, then the area of the triangle ANB is equal to
Updated On: Sep 24, 2024
- \(\frac{1}{2}\)
- \(\frac{2}{3}\)
- \(\frac{1}{6}\)
- \(\frac{5}{3}\)
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The Correct Option is C
Solution and Explanation
The correct option is(C): \(=\frac{1}{6}\)
Tangent toC1 at M: –x + y = 2 ≡T
Intersection of T with C2⇒ (x – 3)2 + x2 = 5
⇒ x = 1, 2
A(1, 3) and B(2, 4)
Let N ≡ (α, β)
Then –x + y = 2 shall be chord of contact for x2 + y2 – 6x – 4y + 8 = 0
\(∴αx+βy-3x-3α-2y-2β+8=0\)
–x + y = 2
After simplification
\(=\frac{1}{6}\) Units.
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Concepts Used:
Distance between Two Points
The distance between any two points is the length or distance of the line segment joining the points. There is only one line that is passing through two points. So, the distance between two points can be obtained by detecting the length of this line segment joining these two points. The distance between two points using the given coordinates can be obtained by applying the distance formula.
