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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 - 3y = 13 5) 2x - 3y = -13 Solution: (5) 2x - 3y = -13... 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 = ±√7 y = mx + 2 and the curve x2 + y2 = 1 x2 + y2 = ((y - mx) / 2)2... 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 + y = 1 Solution: (3) x2 + y2 = 2 The perpendicular from the centre bisects the chord.... 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 perpendicular from (2, 4) on the line x + y + 2 = 0... 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... 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) 3y = x... 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 units... 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... 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... 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 + y = 8 Solution: (2) x + y = 2√2 Given equation of circle is x2 + y2 + 4x - 4y + 4... View Article

The equation of tangents drawn from the origin to the circle x² + y² – 2rx – 2hy + h² = 0 are

1) x = 0, y = 0 2) x = 1, y = 0 3) (h2 - r2)x - 2rhy = 0, y = 0 4) (h2 - r2)x - 2rhy = 0, x = 0 Solution: (4) (h2 - r2)x - 2rhy = 0, x = 0... View Article

The values of λ, so that the line 3x – 4y = λ touches x² + y² – 4x – 8y – 5 = 0 are

1) -35, 15 2) 3, -5 3) 35, -15 4) -3, 5 5) 20, 15 Solution: (1) -35, 15 x2 + y2 - 4x - 8y - 5 = 0 C (- g, - f) = (2, 4) r =... View Article

The equation of the common tangent of the two touching circles, y² + x² – 6x -12y + 37 = 0 and x² + y² – 6y + 7 = 0 is

1) x + y - 5 = 0 2) x - y + 5 = 0 3) x - y - 5 = 0 4) x + y + 5 = 0 Solution: (3) x - y - 5 = 0... 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... 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 = 80... 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 units... 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 is tangent to the circle, then the length of the perpendicular from the... View Article

Tangents are drawn from the point (17, 7) to the circle x² + y² = 169. Statement I The tangents are mutually perpendicular. Statement II The locus of the points from which mutually perpendicular tangents can be drawn to the given circles is x² + y² = 338.

Statement I The tangents are mutually perpendicular Statement II The locus of the points from which mutually perpendicular tangents can be drawn... View Article

If θ is the angle between the tangents from (-1, 0) to the circle x² + y² – 5x + 4y = 0, then θ is equal to

1) 2 tan-1 (7 / 4) 2) tan-1 (7 / 4) 3) 2 cot-1 (7 / 4) 4) cot-1 (7 / 4) Solution: (1) 2 tan-1 (7 / 4)... View Article

The equation of the tangents to the circle x² + y² = 13 at the point whose abscissa is 2, are

1) 2x + 3y = 13, 2x - 3y = 13 2) 3x + 2y = 13, 2x - 3y =1 3 3) 2x + 3y = 13, 3x - 2y = 13 4) None of these above Solution: (1) 2x + 3y = 13,... View Article

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