The equation of circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5, is
1) 6 (x2 + y2) + 5 (3x – 2y) = 0 2) x2 + y2 – 2x – 3y... View Article
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The equation of the circle passing through (4, 5) and having the center (2, 2) is
1) x2 + y2 + 4x + 4y – 5 = 0 2) x2 + y2 – 4x – 4y... View Article
Suppose a circle passes through (2, 2) and (9, 9) and touches the X-axis at P. If O is the origin, then OP is equal to
1) 4 2) 5 3) 6 4) 9 5) 11 Solution: (3) 6 \(\begin{array}{l}\mathbf{r}=\sqrt{(\mathbf{h}-\mathbf{h})^{2}+(\mathbf{k}-\mathbf{0})^{2}}=\mathbf{k}\\ C A=C B=r \\ \rightarrow \mathbf{C... View Article
The equation of the circle with center (2, 1) and touching the line 3x + 4y = 5 is
1) x2 + y2 – 4x – 2y + 5 = 0 2) x2 + y2 – 4x – 2y... View Article
One of the diameter of the circle x2 + y2 – 12x + 4y + 6 = 0 is given by
1) x + y = 0 2) x + 3y = 0 3) x = y 4) 3x + 2y... View Article
The other end of the diameter through the point (-1, 1) on the circle x2 + y2 – 6x + 4y – 12 = 0 is
1) (-7, 5) 2) (-7, – 5) 3) (7, – 5) 4) (7, 5) Solution: (3) (7, – 5) \(\begin{array}{l}x^{2}+y^{2}-6... View Article
The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0, is
1) x2 + y2 – 6x + 6y + 9 = 0 2) x2 + y2 – 6x – 6y... View Article
The equation of two circles which touch the Y – axis at (0, 3) and make an intercept of 8 units on X – axis , are
1) x2 + y2 ± 10x – 6y + 9 = 0 2) x2 + y2 ± 6x – 10y... View Article
A variable circle passes through the fixed point A (p, q) and touches X – axis. The locus of the other end of the diameter through A is
1) (x – p )2 = 4qy 2) (x – q )2 = 4py 3) (y – p )2 =... View Article
The area of the circle centred at (1, 2) and passing through (4, 6) is
1) 5 π sq units 2) 10 π sq units 3) 25 π sq units 4) None of these Solution:... View Article
The center of the circle whose normals are x2 – 2xy – 3x + 6y = 0, is
1) (3, 3 / 2) 2) (3, – 3 / 2) 3) (3 / 2, 3) 4) None of these... View Article
If the line y = 7x – 25 meets the circle x2 + y2 = 25 in points A, B, then the distance between A and B is
1) √10 2) 10 3) 5√2 4) 5 Solution: (3) 5√2 y = 7x – 25 …(i) x2 + y2... View Article
The locus of the centre of a circle, which touches externally the circle x2 + y2 – 6x – 6y + 14 = 0 and also touches the y-axis, is given by the equation:
1) x2 – 6x – 10y + 14 = 0 2) x2 – 10x – 6y + 14 = 0... View Article
The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is
1) (3 / 2, 1 / 2) 2) (1 / 2, 3 / 2) 3) (1 / 2, 1 /... View Article
The equation of the smallest circle passing through the points (2, 2) and (3, 3) is
1) x2 + y2 + 5x + 5y + 12 = 0 2) x2 + y2 – 5x – 5y... View Article
If one end of the diameter is (1, 1) and the other end lies on the line x + y = 3, then locus of centre of circle is
1) x+ y = 1 2) 2(x – y ) = 5 3) 2x + 2y = 5 4) None... View Article
If the lines 2x – 3y = 5 and 3x – 4y = 7 are two diameters of a circle of radius 7, then the equation of the circle is
1) x2 + y2 + 2x – 4y – 47 = 0 2) x2 + y2 = 49 3) x2... View Article
The radius of the circle with the polar equation r2 – 8r(√3 cos θ + sin θ) + 15 = 0 is
1) 8 2) 7 3) 6 4) 5 Solution: (2) 7 \(\begin{array}{l}\begin{array}{l} \mathbf{r}^{2}-8r(\sqrt{3} \cos \theta+\sin \theta)+15=0\\ \text { or }... View Article
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is
1) (3, 4) 2) (3, – 4) 3) (-3, 4) 4) (-3, – 4) Solution: (4) (-3, – 4) The... View Article
If the tangent at point P on the circle x2 + y2 + 6x + 6y – 2 = 0 meets the straight line 5x – 2y + 6 = 0 at a point Q on y – axis, the length of PQ is
1) 4 2) 2√5 3) 5 4) 3√5 Solution: (3) 5 The line 5x – 2y + 6 = 0... View Article
