Conic Section

Question

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

x² + y² – 3ax – 4by + (a² + b² – p² ) = 0

2ax + 2by – (a² – b² + p² ) = 0

x² + y² – 2ax – 3by + (a² – b² – p² ) = 0

2ax + 2by – (a² + b² + p² ) = 0

Solution

2ax + 2by – (a² + b² + p² ) = 0

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.

For Daily Free Study Material Join wiredfaculty

Conic Section

Some More Questions From Conic Section Chapter

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

If the lines 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location