SATHEE: Circle 3 Question 8

Circle 3 Question 8

8. 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 $P Q$ is

$(2002, 1 M)$

(a) 4

(b) $2 \sqrt{5}$

(d) $3 \sqrt{5}$

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Answer:

Correct Answer: 8. (c)

Solution:

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

$\begin{aligned} = \sqrt{x_{1}^{2} + y_{1}^{2} + 6 x_{1} + 6 y_{1} - 2} \\ = \sqrt{0^{2} + 3^{2} + 6 (0) + 6 (3) - 2} \\ = \sqrt{25} = 5 \end{aligned}$

Circle 3 Question 8

8. 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 $P Q$ is

Answer:

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Circle 3 Question 8

8. 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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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8. 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 $P Q$ is