The focal chord of y2 = 16x is tangent to (x – 6)2 + y2 = 2, then the possible values of the slope of this chord, are
Focus (a, 0) is (4, 0). Any focal chord is
y – 0 = m(x – 4)
or mx – y – 4m = 0.
Apply the condition of tangency p = t with circle (6, 0), .
or 2m2 = m2 + 1 m2 = 1
The vertex of a parabola is the point (a, b) and latus-rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equation is
Slope of common tangent to parabolas y2 = 4x and x2 = 8y is
If a focal chord with positive slope of the parabola y2 = 16xtouches the circle x2 + y2 – 12x + 34 = 0, then m is
If 2y = x + 24 is a tangent to parabola y2 = 24x, then its distance from parallel normal is
PQ is a focal chord of the parabola y2 = 4ax, O is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.
Find the shortest distance between the circle x2 + y2 – 24y + 128 = 0 and the parabola y2 = 4x.
The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is
If the line x – 1 = 0 is the directrix of the parabola y2 – ky + 8 = 0, then one of the of the value of k is
Equation of the parabola whose axis is y = x distance from origin to vertex is and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :
The curve described parametrically by x = t2 + t + 1, y = t2 – t + 1 represents.