Question

P3,2 is a point on the circle x' + y2 = 13. Two points A, B
are on the circle such that PA= PB = 15. The equation of
chord AB is
​

Answer 1

Answer:

the answer is 65/72

Step-by-step explanation:

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Answer 2

6x + 4y + 21 = 0 is the equation of the chord.

Given,

Equation of circle → x² + y² = 13

Point → P(3, 2)

PA = PB = √5

To Find,

Equation of the chord AB

Solution,

Comparing with the general equation of the circle we get,

Center → O(0,0)

Radius → $\sqrt{13}$ units

Let the points be A(a, b) and B(c, d)

According to the question,

Distance of P from A = Distance of P from B = 15

PA = PB = √5

Also, C is the center of the circle, and P, A, and B lie on the circle

OP = OA = OB = $\sqrt{13}$ units

AB ⊥ OP

AO = 15 Cos x

Also, AO = $\sqrt{13}$ Sin 2x

15 Cos x = $\sqrt{13}$ * 2 * Sin x Cos x

Sin x = √5/2√13

DP = √5 Sin x

DP = 5/2√13

OD = √13 - 5/2√13

OD = 21/2√13

Now,

x = $\frac{21*3 + 5*0}{21+5} = \frac{ 63}{26}$

y = $\frac{21*2+5*0}{21+5} = \frac{42}{26}$

Slope of OP = $\frac{\frac{42}{26} }{\frac{63}{26} }$ = $\frac{2}{3}$

Slope of AB = $\frac{-1}{\frac{2}{3} } = \frac{-3}{2}$

Therefore equation,

(y - 42/26) = -3/2 * (x - 63/26)

2y + 3x = -21/2

6x + 4y + 21 = 0 is the required equation.

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