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If two chords having lengths a² – 1 and 3(a + 1), where a is a constant of a circle bisect each other, then the radius of the circle is

1) 6 2) 15/2 3) 8 4) 19/2 5) 10 Solution: (2) 15/2 As both the chords are diameters, ⇒... View Article

The locus of the mid – points of the chords of the circle x² + y² = 4 which subtend a right angle at the origin is

1) x2 + y2 = 1 2) x2 + y2 = 2 3) x + y = 1 4) x... View Article

The radius of the circle, which is touched by the line y = x and has its centre on the positive direction of the x-axis and also cuts-off a chord of length 2 units along the line √3y – x = 0 is

1) √5 2) √3 3) √2 4) 1 Solution: (3) √2 \(\begin{array}{l}\text \ Let \ (\mathrm{g}, \mathrm{o}) \ be \... View Article

The equation of the chord of the circle x² + y² = 81, which is bisected at the point (-2, 3), is

1) 3x – y = 13 2) 3x – 4y = 13 3) 2x – 3y = 13 4) 3x... View Article

If the lines joining the origin to the intersection of the line y = mx + 2 and the circle x² + y² = 1 are at right angles, then

1) m = √3 2) m = ±√7 3) m = 1 4) m = √5 Solution: (2) m =... View Article

The locus of the mid – points of the chord of the circle x² + y² = 4 which subtends a right angle at the origin is

1) x + y = 2 2) x2 + y2 = 1 3) x2 + y2 = 2 4) x... View Article

A circle with centre at (2, 4) is such that the line x + y + 2 = 0 cuts a chord of length 6. The radius of the circle is

1) √41 cm 2) √11 cm 3) √21 cm 4) √31 cm Solution: (1) √41 cm The length of the... View Article

The measure of the chord intercepted circle x² + y² = 9 and the line x – y + 2 = 0 is

1) √28 2) 2√5 3) 7 4) 5 Solution: (1) √28 \(\begin{array}{l}\mathbf{x}_{1}=-\frac{\mathbf{2}+\sqrt{\mathbf{1 4}}}{\mathbf{2}} \\ \mathbf{y}_{1}=\frac{\mathbf{2}+\sqrt{\mathbf{1 4}}}{\mathbf{2}}\\ \mathbf{x}_{2}=-\frac{\mathbf{2}-\sqrt{\mathbf{1 4}}}{\mathbf{2}} \\ \mathbf{y}_{2}=\frac{\mathbf{2}-\sqrt{\mathbf{1... View Article

If y = 3x is the tangent to a circle with centre (1, 1), then the other tangent drawn through (0, 0) to the circle is

1) 3y = x 2) y = – 3x 3) y = 2x 4) y = – 2x Solution: (1)... View Article

Two tangents to the circle x² + y² = 4 at the points A and B meet at P(-4, 0). The area of the quadrilateral PAOB, where O is the origin, is

1) 4 sq units 2) 6√2 sq units 3) 4√3 sq units 4) None of these Solution: (3) 4√3 sq... View Article

Angle between tangents drawn to circles x² + y² = 20, from the point (6, 2) is

1) π/2 2) π 3) π/4 4) 2π Solution: (1) π/2 \(\begin{array}{l}\text \ The \ equation \ of \ tangent... View Article

If x/α + y/β = 1 touches the circles x² + y² = a², then point (1/α, 1/β) lies on

1) straight line 2) circle 3) parabola 4) ellipse Solution: (2) circle \(\begin{array}{l}\text \ If \ line \ \frac{x}{\alpha}+\frac{y}{\beta}=1 \... View Article

The equation of the tangent to the circle x² + y² + 4x – 4y + 4 = 0 which makes equal intercepts on the positive coordinates axes, is

1) x + y = 2 2) x + y = 2√2 3) x + y = 4 4) x... View Article

If the equation of tangent to the circle x² + y² – 2x + 6y – 6 = 0 and parallel to 3x – 4y + 7 = 0 is 3x – 4y + k = 0, then the values of k are

1) 5, -35 2) -5, 35 3) 7, -32 4) -7, 32 Solution: (1) 5, -35 \(\begin{array}{l}\text \ The \... View Article

The condition for a line y = 2x + c to touch the circle x² + y² = 16 is

1) c = 10 2) c2 = 80 3) c = 12 4) c2 = 64 Solution: (2) c2 =... View Article

From the point P(16, 7), tangents PQ and PR are drawn to circle x² + y² – 2x – 4y – 20 = 0. If C is the centre of the circle, then the area of equilateral PQCR is

1) 450 sq units 2) 15 sq units 3) 50 sq units 4) 75 sq units Solution: (4) 75 sq... View Article

If 3x + y + k = 0 is a tangent to the circle x² + y² = 10, then the values of k are

1) ± 7 2) ± 5 3) ± 10 4) ± 9 Solution: (3) ± 10 If the given line... View Article

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