Analytic Geometry 2D Mock Tests

A circle C has centre at the intersection of the lines x + y = 4 and x - y = 0, and it touches the line x + y = 10. The radius of C is

The locus of the point of intersection of perpendicular tangents to the parabola y² = 8x is:

The line y = 2x + 1 is tangent to a circle with center at (1, k) and touches the circle at point A. If AB is a diameter of the circle and B lies on the x-axis, then the value of k is:

The length of the focal chord of the parabola y^2 = 4ax which makes an angle of pi/4 with the positive x-axis is

Two circles with centres at (3, 0) and (0, 4) touch each other externally. If the radius of the first circle is 2, then the radius of the second circle is

A line y = 2x touches a circle with centre (0, α), α > 0 at point A₁. B₁ is a point on the circle such that A₁B₁ is a diameter. If the line through B₁ perpendicular to y = 2x intersects the x-axis at (3, 0), then α equals:

The parabola y^2 = 4ax has a point P = (at^2, 2at). If the tangent at P meets the directrix at T, then the angle PTF at the focus F is:

An ellipse is drawn with major axis of length 10 and minor axis of length 8. A parabola is drawn such that its vertex coincides with the nearest vertex of the ellipse and focus coincides with the focus of the ellipse. The length of the latus rectum of the parabola is equal to: