Analytic Geometry 2D Mock Tests

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

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:

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:

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 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

A focal chord of the parabola y^2 = 4ax makes an angle of pi/4 with the positive x-axis. The length of this focal chord 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: