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

Question

If the tangent at the point P on the circle x2+y2+6 x+6 y=2 meets the straight line 5 x-2 y+6=0 at a point Q on the y-axis, then the length of P Q is (A) 4 (B) 2 √5 (C) 5 (D) 3 √5

Tardigrade Admin · Accepted Answer

The line 5 x-2 y+6=0 meets the y-axis at the point (0,3) and therefore the tangent has to pass through the point (0,3) and required length is therefore, =√x12+y12+6 x1+6 y1-2 =√0+32+6(0)+6(3)-2 =√25=5

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

4

$25$

5

$35$

The line $5 x - 2 y + 6 = 0$ meets the $y$ -axis at the point $(0, 3)$ and therefore the tangent has to pass through the point $(0, 3)$ and required length is therefore,
$= x_{1}^{2} + y_{1}^{2} + 6 x_{1} + 6 y_{1} - 2$
$= 0 + 3^{2} + 6 (0) + 6 (3) - 2$
$= 25 = 5$

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

4

25​

5

35​

The line 5x−2y+6=0 meets the y-axis at the point (0,3) and therefore the tangent has to pass through the point (0,3) and required length is therefore, =x12​+y12​+6x1​+6y1​−2​ =0+32+6(0)+6(3)−2​ =25​=5

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

$25$

$35$

The line $5 x - 2 y + 6 = 0$ meets the $y$ -axis at the point $(0, 3)$ and therefore the tangent has to pass through the point $(0, 3)$ and required length is therefore,
$= x_{1}^{2} + y_{1}^{2} + 6 x_{1} + 6 y_{1} - 2$
$= 0 + 3^{2} + 6 (0) + 6 (3) - 2$
$= 25 = 5$