Question

the equation of the chord of contact of the point (4,2) with respect to circle x²+y²-5x+4y-3=0​

Answer 1

We have to find the equation of chord of contact of the point (4,2) with respect to circle x² + y² - 5x + 4y - 3 = 0.

Solution : concept : equation of chord of contact of point (x₁, y₁) with respect of circle x² + y² + 2gx + 2fy + c is given by, xx₁ + yy₁ + g(x + x₁) +f(y + y₁) + c = 0

Here, (x₁, y)₁ = (4,2)

And x² + y² + 2gx + 2fy + c = 0 = x² + y² -5x + 4y - 3

So equation chord of contact :

x(4) + y(2) - 5/2 (x + 4) + 2(y + 2) - 3 = 0

⇒4x + 2y - 5x/2 - 10 + 2y + 4 - 3 = 0

⇒8x + 4y - 5x - 20 + 4y + 2 = 0

⇒3x + 8y - 18 = 0

Therefore the equation of chord of contact is 3x + 8y - 18 = 0

Answer 2

Answer :-

We have to find the equation of chord of contact of the point (4,2) with respect to circle x² + y² - 5x + 4y - 3 = 0.

Solution :

concept : equation of chord of contact of point (x₁, y₁) with respect of circle x² + y² + 2gx + 2fy + c is given by, xx₁ + yy₁ + g(x + x₁) +f(y + y₁) + c = 0

Here,

(x₁, y)₁ = (4,2) And

x² + y² + 2gx + 2fy + c = 0 = x² + y² -5x + 4y - 3

So equation chord of contact :

x(4) + y(2) - 5/2 (x + 4) + 2(y + 2) - 3 = 0

⇒4x + 2y - 5x/2 - 10 + 2y + 4 - 3 = 0

⇒8x + 4y - 5x - 20 + 4y + 2 = 0

⇒3x + 8y - 18 = 0

Therefore the equation of chord of contact is 3x + 8y - 18 = 0

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