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Construction of Tangent When Point is on the Circle

If the tangen...

Question

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 point $Q$ on the $y$ -axis, then the length of $P Q$ is

4

units

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2 \sqrt{5}

units

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5

units

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3 \sqrt{5}

units

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Solution

The correct option is C $5$ units
$5 x - 2 y + 6 = 0$
$y$ -intercept of the line is $Q (0, 3) .$
So tangent at $P$ on $x^{2} + y^{2} + 6 x + 6 y - 2 = 0$ passes through $Q (0, 3)$ as per the given condition.

$∴ P Q =$ length of tangent to circle from $(0, 3)$
$= \sqrt{S_{1}} = 5$ units

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Similar questions

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 point

Q

on the

y

-axis, then the length of

P Q

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 point

Q

on the y-axis, then the length of

P Q

is.

Q. If the tangent at the 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 point

Q

on the

y

-axis, then the length of

P Q

Q. lf 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

Q. If the tangent at the point

P

on the circle

x^{2} + y^{2} + 6 x + 6 y = 2

meets the line

5 x - 2 y + 6 = 0

at a point

Q

on the

y -

axis, then the length of

P Q =

-______

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

The correct option is C 5 units5x−2y+6=0 y-intercept of the line is Q(0,3). So tangent at P on x2+y2+6x+6y−2=0 passes through Q(0,3) as per the given condition. ∴PQ= length of tangent to circle from (0,3) =√S1=5 units

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 point $Q$ on the $y$ -axis, then the length of $P Q$ is

The correct option is C $5$ units
$5 x - 2 y + 6 = 0$
$y$ -intercept of the line is $Q (0, 3) .$
So tangent at $P$ on $x^{2} + y^{2} + 6 x + 6 y - 2 = 0$ passes through $Q (0, 3)$ as per the given condition.

$∴ P Q =$ length of tangent to circle from $(0, 3)$
$= \sqrt{S_{1}} = 5$ units