Question

The lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 square units. An equation of this circle is (π = 22/7)

Solution

Correct option is

x2 + y2 – 2x + 2y = 47

The centre of the circle is the point of intersection of the given diameters 2x – 3y = 5 and 3x – 4y = 7, which is (1, –1) and if r is the radius of the circle,  

  

Hence an equation of the required circle is  

SIMILAR QUESTIONS

Q1

The circle passing through the distinct points (1, t), (t, 1) and (tt) for all values of t, passes through the point

Q2

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Q3

The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α. The equation of the locus of the point P is

Q4

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Q5

If a line segment AM = a moves in the plane XOY remaining parallel toOX so that the left end point A slides along the circle x2 + y2 = a2, the locus of M is

Q6

If common chord of the circle C with centre at (2, 1) and radius r and the circle x2 + y2 – 2x – 6y + 6 = 0 is a diameter of the second circle, then the value of r is  

Q7

Tangents drawn from the point P(1, 8) to the circle x2 + y2 – 6x – 4y – 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle in PAB is

Q8

Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

Q9

An equilateral triangle is inscribed in the circle x2 + y2 = a2 with the vertex at (a, 0). The equation of the side opposite to this vertex is

Q10

The equation f a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is