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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... 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... 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... View Article

If the line y cos α = xsin α + a cos α is a tangent to the circle x² + y² = a², then

1) sin2 α = 1 2) cos2 α = 1 3) sin2 α = a2 4) cos2 α = a2... View Article

The angle between the tangents drawn at the points (5, 12) and (12, – 5) to the circles x² + y² = 169 is

1) 45o 2) 60o 3) 30o 4) 90o Solution: (4) 90o x2 + y2 = 169 Differentiating w.r.t x 2x... View Article

Locus of the point of intersection of perpendicular tangents to the circle x² + y² = 16 is

1) x2 + y2 = 8 2) x2 + y2 = 32 3) x2 + y2 = 64 4) x2... View Article

The equation of the tangent from the point (0, 1) to the circle x² + y² – 2x – 6y + 6 = 0, is

1) 3 (x2 − y2) + 4xy − 4x − 6y + 3 = 0 2) 3y2 + 4xy −... View Article

The equation of normal of x² + y² – 2x + 4y – 5 = 0 at (2, 1) is

1) y = 3x – 5 2) 2y = 3x – 4 3) y = 3x + 4 4) y... View Article

The length (in units) of tangent from point (5, 1) to the circle x² + y² + 6x – 4y – 3 = 0 is

1) 81 2) 29 3) 7 4) 21 Solution: (3) 7 \(\begin{array}{l}\begin{array}{l} \text { Length of tangent from }(5,1) \text... View Article

The equation of the two tangents from (- 5, – 4) to the circle x² + y² + 4x + 6y + 8 = 0 are

1) x + 2y + 13 = 0, 2x – y + 6 = 0 2) 2x + y +... View Article

The circles x² + y² + 4x – 4y + 4 = 0 touches

1) X – axis 2) Y – axis 3) X – axis and Y – axis 4) None of these... View Article

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (≠ 1). Then, its locus is a

1) parabola 2) circle 3) hyperbola 4) pair of straight lines Solution: (2) circle \(\begin{array}{l}\text { Let two coplanar points... View Article

Which of the following equations given circle?

1) r = 2 sin θ 2) r2 cos 2θ = 1 3) r( 4 cos θ + 5 sin... View Article

The locus of the centre of the circle for which one end of a diameter is (1, 1) while the other end is in the line x + y = 3 is

1) x+ y = 1 2) 2(x – y) = 5 3) 2x + 2y = 5 4) None of... View Article

The radius of the circle x² + y² + 4x + 6y + 13 = 0 is

1) √26 2) √13 3) √23 4) 0 Solution: (4) 0 x2 + y2 + 4x + 6y + 13... View Article

The radius of any circle touching the lines 3x – 4y + 5 = 0 and 6x – 8y – 9 = 0 is

1) 1.9 2) 0.95 3) 2.9 4) 1.45 Solution: (2) 0.95 \(\begin{array}{l}3 \mathrm{x}-4 \mathrm{y}+5=0 \text \ and \ 3 \mathrm{x}-4... View Article

Find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.

1) x2 + y2 + 3x + 4y = 0 2) x2 + y2 + 3x – 4y = 0... View Article

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