If the line `y-sqrt3x+3=0` cuts the parabola `y^2=x+2` at `P` and `Q` then `AP.AQ` is equal to

The circle C1 : x^2 + y^2 = 3 , with center at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2sqrt(3) and centers Q2 and Q3, respectively.If Q_2 and Q_3 lies on the y-axis, then

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in first and fourth quadrant respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S. The radius of the circumcircle of the triangle PRS is-

The directrix of the parabola y^(2) + 4x + 3 = 0 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.

A line is drawn from A(-2,0) to intersect the curve y^2=4x at P and Q in the first quadrent such that 1/(AP)+1/(AQ)lt1/4 . Then the slope of the line is always

What is the focus of the parabola x^2+y^2+2xy−6x−2y+3=0 .

Find the area of the region enclosed by the parabola y^2 = 9x and the line y = 3x .

A straight line through the point (2, 2) intersects the lines sqrt3x + y = 0 and sqrt3 x-y=0 at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is ,

Let (x,y) be any point on the parabola y^2= 4x . Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is: