The circle `x^2 + y^2 -2x - 4y+1=0` with centre C meets the y axis at points A and B. Find the area of the triangle ABC.

Tangents drawn from the point P(1,8) to the circle x^(2)+y^(2)-6x-4y-11=0 touch the circle at points A and B. The equation of the cricumcircle of triangle PAB is

The circle x^2 + y^2+ 4x-7y + 12 = 0 cuts an intercept on y-axis equal to

Let A be the centre of the circle x^2+y^2-2x-4y-20=0 . If the tangents at the points B (1, 7) and D(4,-1) on the circle meet at the point C find the area of the quadrilateral ABCD.

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , then find the equation of the circle on A B as diameter.

An ellipse is drawn by taking a diameter of the circle (x-1)^2+y^2=1 as its semi-minor axis and a diameter of the circle x^2+(y-2)^2=4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is (1) 4x^2+""y^2=""4 (2) x^2+""4y^2=""8 (3) 4x^2+""y^2=""8 (4) x^2+""4y^2=""16

Tangents are drawn to the circle x^2+y^2=50 from a point "P lying on the x-axis. These tangents meet the y-axis at points 'P_1,' and 'P_2 . Possible co-ordinates of 'P' so that area of triangle PP_1P_2 is minimum is/are -

Statement 1 : The area of the ellipse 2x^2+3y^2=6 is more than the area of the circle x^2+y^2-2x+4y+4=0 . Statement 2 : The length f the semi-major axis of an ellipse is more that the radius of the circle.

The centre of the circle x^(2)+y^(2)-6x+4y-1=0 is

A normal inclined at 45^@ to the axis of the ellipse x^2 /a^2 + y^2 / b^2 = 1 is drawn. It meets the x-axis & the y-axis in P & Q respectively. If C is the centre of the ellipse, show that the area of triangle CPQ is (a^2 - b^2)^2/(2(a^2 +b^2)) sq units