Equation of chord AB of circle x 2- y 2-2 passing through P 2-2 such that PB - PA -3- is given byA- x-3 yB- x-y - y-2-3x-2D- none of these

The correct option is B Let P = (2, 2) PB/PA = 3 ⇒ PB = 3.PA We have PA.PB = S_11 ⇒ 3 PA^2 = 6 ⇒ PA = √(2)⇒ PB = 3 √(2) ∴ A = (2 √(2) cos θ, 2 √(2) sin θ) ...

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Standard IX

Mathematics

Equation of a Chord Joining Two Points with Circle in Parametric Form

Equation of c...

Question

Equation of chord AB of circle $x^{2} + y^{2} = 2$ passing through P(2, 2) such that $\frac{P B}{P A} = 3$ , is given by

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Solution

The correct option is B

Let P = (2, 2)
$\frac{P B}{P A} = 3 \Rightarrow P B = 3. P A$
We have $P A . P B = S_{11}$
$\Rightarrow 3 P A^{2} = 6$
$\Rightarrow P A = \sqrt{2} \Rightarrow P B = 3 \sqrt{2}$
$∴ A = (2 - \sqrt{2} c o s θ, 2 - \sqrt{2} s i n θ)$ lies on circle
$∴ (2 - \sqrt{2} c o s θ)^{2} + (2 - \sqrt{2} s i n θ)^{2} = 2$
$\Rightarrow c o s θ + s i n θ = \sqrt{2}$
$\Rightarrow θ = \frac{π}{4}$
$∴$ slope of AB = 1
$∴$ Equation of AB is x = y

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Equation of chord AB of circle x2+y2=2 passing through P(2, 2) such that PBPA=3, is given by

The correct option is B Let P = (2, 2) PBPA=3⇒PB=3.PA We have PA.PB=S11 ⇒3PA2=6 ⇒PA=√2⇒PB=3√2 ∴A=(2−√2cosθ,2−√2sinθ) lies on circle ∴(2−√2cosθ)2+(2−√2sinθ)2=2 ⇒cosθ+sinθ=√2 ⇒θ=π4 ∴ slope of AB = 1 ∴ Equation of AB is x = y

Equation of chord AB of circle $x^{2} + y^{2} = 2$ passing through P(2, 2) such that $\frac{P B}{P A} = 3$ , is given by