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

Question

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

Tardigrade Admin · Accepted Answer

x2+y2+6 x+6 y-2 =0 Centre (-3-3) radius =√9+9+2 =√20 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f81924ffd1e0c235d01655ea10518905-.png" /> Now, Q C=√(-3)2+62=√45 In right Δ C P Q P Q=√45-20=5

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

4

$25$

5

$35$

$x^{2} + y^{2} + 6 x + 6 y - 2 = 0$
Centre $(- 3 - 3)$ radius $= 9 + 9 + 2$
$= 20$

Now, $QC = (- 3)^{2} + 6^{2} = 45$
In right $Δ CPQ$
$PQ = 45 - 20 = 5$

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

4

25​

5

35​

x2+y2+6x+6y−2=0 Centre (−3−3) radius =9+9+2​ =20​ Now, QC=(−3)2+62​=45​ In right ΔCPQ PQ=45−20​=5

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

$25$

$35$

$x^{2} + y^{2} + 6 x + 6 y - 2 = 0$
Centre $(- 3 - 3)$ radius $= 9 + 9 + 2$
$= 20$

Now, $QC = (- 3)^{2} + 6^{2} = 45$
In right $Δ CPQ$
$PQ = 45 - 20 = 5$