Find The Equation If The Circle The End Points Of Whose Diameter Are The Centres Of The Circle x2 + y2 + 6x – 14y = 1 And x2 + y2 – 4x + 10y = 2.

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Question

Find the equation if the circle the end points of whose diameter are the centres of the circle x² + y² + 6x – 14y = 1 and x² + y² – 4x + 10y = 2.

easy

Solution

Correct option is

x² + y² + x – 2y – 41 = 0

The centres of the given circles

x² + y² + 6x – 14y – 1 = 0

and x² + y² – 4x + 10y – 2 = 0 are (–3, 7) and (2, –5) are the extremities of the diameter of required circle.

Hence equation of circle is

(x + 3) (x – 2) + (y – 7) (y + 5) = 0

⇒ x² + y² + x – 2y – 41 = 0

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SIMILAR QUESTIONS

Q1

Find the equation of chord of x² + y² – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

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Q2

Find the equation of that chord of the x² + y² = 15 which is bisected at (3, 2).

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Q3

Find the centre and radius of the circle

2x² + 2y² = 3x – 5y + 7

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Q4

Find the equation of the circle whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 and passes through the origin.

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Q5

Find the equation of the circle concentric with the circle x² + y² – 8x + 6y– 5 = 0 and passing through the point (–2, –7).

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Q6

A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of the circle if it passes through (7, 3).

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Q7

Find the area of an equilateral triangle inscribed in the circle

x² + y² + 2gx + 2fy + c = 0

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Q8

Find the parametric form of the equation of the circle

x² + y² + px + py = 0

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Q9

If the parametric of form of a circle is given by

(i) x = – 4 + 5 cos θ and y = – 3 + 5 sin θ

(ii) x = a cos α + b sin α and y = a sin α – b cos α

Find its Cartesian form.

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Q10

The sides of a square are x = 2, x = 3, y = 1and y = 2. Find the equation of the circle drawn on the diagonals of the square as its diameter.

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