If the tangent at the point P on the circle x 2 + y 2 + 6 x + 6 y = 2 meets a straight line 5 x - 2 y + 6 = 0 at a point Q on the y -axis, then the length of P Q is [2002]

Question

If the tangent at the point $P$ on the circle $x^{2} + y^{2} + 6 x + 6 y = 2$ meets a straight line $5 x - 2 y + 6 = 0$ at a point $Q$ on the $y$ -axis, then the length of $P Q$ is [2002]

Smart Achievers · Accepted Answer

(3)

Given that line $x^{2} + y^{2} + 6 x + 6 y = 2$ is intersected by tangent at $P$ to the circle $x^{2} + y^{2} + 6 x + 6 y - 2 = 0$ on $P Q$ -axis at $Q (0, 3)$ .

This means that tangent passes through (0, 3)

$∴$ $P Q = length of tangent to circle from (0, 3)$

$= \sqrt{0^{2} + 3^{2} + 6 (0) + 6 (3) - 2} = \sqrt{0 + 9 + 0 + 18 - 2} = \sqrt{25} = 5$

Solution

Q.
If the tangent at the point $P$ on the circle $x^{2} + y^{2} + 6 x + 6 y = 2$ meets a straight line $5 x - 2 y + 6 = 0$ at a point $Q$ on the $y$ -axis, then the length of $P Q$ is [2002]

1 $4$

2 $2 \sqrt{5}$

3 $5$

4 $3 \sqrt{5}$

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Solution

Q. If the tangent at the point P on the circle x2+y2+6x+6y=2 meets a straight line 5x-2y+6=0 at a point Q on the y-axis, then the length of PQ is [2002]

1 4

2 25

3 5

4 35