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Grade 12Algebra

If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is ?

sudhanshu

12 Years agoGrade 12

3 Answers

SHAIK AASIF AHAMED

12 Years ago

Hello student,

Let the centre be (α, β)
∵It cut the circle x² + y² = p² orthogonally
2(-α) × 0 + 2(-β) × 0 = c1 – p²
c1 = p²
Let equation of circle is x² + y² - 2αx - 2βy + p² = 0
It pass through (a, b) ⇒ a²+ b²- 2αa - 2βb + p² = 0
Locus ∴ 2ax + 2by – (a² + b² + p²) = 0.

Thanks and Regards

Shaik Aasif

askIITians faculty

sajan Saran

9 Years ago

Let the centre be (α, β)It cut the circle x2 + y2 = p2 orthogonally2(-α) × 0 + 2(-β) × 0 = c – p2c = p2Let equation of circle is x2 + y2 + 2αx +2βy + p2 = 0It pass through (a, b) ⇒ a2+ b2+2αa +2βb + p2 = 0Locus ∴ 2ax + 2by + (a2 + b2 + p2) = 0.

Kushagra Madhukar

5 Years ago

Dear student,

Please find the attached solution to your problem below.

Let the centre be (α, β)

∵It cut the circle x² + y² = p² orthogonally

2(-α) × 0 + 2(-β) × 0 = c1 – p²

c1 = p²

Let equation of circle is x² + y² - 2αx - 2βy + p² = 0

It passes through (a, b) ⇒ a²+ b²- 2αa - 2βb + p² = 0

Locus ∴ 2ax + 2by – (a² + b² + p²) = 0.

Thanks and regards,

Kushagra

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