Find the equation of the chord of contact of the point $(1, 2)$ with respect to the circle $x^{2} + y^{2} + 2 x + 3 y + 1 = 0$

4 x + 7 y + 10 = 0

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4 x - 7 y + 10 = 0

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7 x + 4 y + 10 = 0

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7 x - 4 y + 10 = 0

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Solution

The correct option is A $4 x + 7 y + 10 = 0$
Equation of chord of contact to the given circle from point $(1, 2)$ is given by,
$T = 0 \Rightarrow 1. x + 2. y + 1. (x + 1) + \frac{3}{2} (y + 2) + 1 = 0$
$\Rightarrow 4 x + 7 y + 10 = 0$

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Similar questions

Find the equation of family of circles through the intersection of $x^{2} + y^{2} - 6 x + 2 y + 4 = 0$ and $x^{2} + y^{2} + 2 x - 4 y - 6 = 0$ whose center lies on $y = x .$

Q. If the abscissas and ordinates of two points

P

and

Q

are the roots of the equations

x^{2} - 7 x + 10 = 0

and

x^{2} + 7 x + 12 = 0

respectively, then the equation of the circle with

P Q

as diameter is

Q. The equation of the obtuse angle bisector of lines

12 x - 5 y + 7 = 0

and

3 y - 4 x - 1 = 0

Q. Orthocentre of the triangle whose sides are given by 4x - 7y + 10 = 0, x + y - 5 = 0 & 7x + 4y - 15 = 0 is

Q. Three sides of a triangle are given by the equations

4 x - 7 y + 10 = 0, x + y = 5

and

7 x + 4 y - 15 = 0

Then, which of the following lies on the line

2 x + 3 y - 8 = 0

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Find the equation of the chord of contact of the point (1,2) with respect to the circle x2+y2+2x+3y+1=0

The correct option is A 4x+7y+10=0Equation of chord of contact to the given circle from point (1,2) is given by, T=0⇒1.x+2.y+1.(x+1)+32(y+2)+1=0⇒4x+7y+10=0

Find the equation of the chord of contact of the point $(1, 2)$ with respect to the circle $x^{2} + y^{2} + 2 x + 3 y + 1 = 0$

The correct option is A $4 x + 7 y + 10 = 0$
Equation of chord of contact to the given circle from point $(1, 2)$ is given by,
$T = 0 \Rightarrow 1. x + 2. y + 1. (x + 1) + \frac{3}{2} (y + 2) + 1 = 0$
$\Rightarrow 4 x + 7 y + 10 = 0$