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

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:

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:

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

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 line y = 2x touches the circle with center (0, alpha), alpha > 0, at point A1. B1 is a point on the circle such that A1B1 is a diameter. If the line B1C1 touches the circle at B1 and meets the x-axis at point C1, and the distance OC1 = 4 (where O is the origin), then alpha is equal to:

The ellipse x^2/a^2 + y^2/b^2 = 1 (a > b) passes through the point (1, 3/2). If its eccentricity is 1/2, then the value of a^2 + b^2 is

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