The number of values of c such that the straight line y = 4x + ctouches the curve , is  


Correct option is


We know that the line y = mx + c touches the curve  iff c2 = a2m2 + b2




If SY and S1Y1 be perpendiculars from the foci upon the tangent atP of an ellipse, then Y and Y1 lie on the auxiliary circle andSY.S1Y1 =    


Find the condition on a and b for which two distinct chords of the ellipse  passing through (a, –b) are bisected by the line x + y = b


Let P be a point on the ellipse , 0 < b < a. Let the line parallel to y-axis passes through P meet the circle  at the point Q, such that P and Q are the same side of x-axis. For two positive  real numbers r and s, find the locus of the point Ron PQ such that PR : RQ = r : s as P varies over the ellipse.  


Consider the family of circle x2 + y2 = r2, 2 < r < 5. If in the first quadrant the common tangent to a circle of the family and the ellipse 4x2 + 25y2 = 100 meets the coordinate axes at A and B, then find the equation of the locus of the mid point of AB.


The orbit of earth is an ellipse with eccentricity 1/60 with the sun at one focus the major axis being approximately 186 × 106 miles in length. Find the shortest and longest distance of the earth from the sun.   



A straight line PQ touches the ellipse  and the circle x2 + y2 = r(b < r < a). RS is a focal chord of the ellipse. If RSis parallel to PQ and meets the circle at points R and S. Find the length of RS


If α and β are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is 


, then the chord joining two points θ1 and θ2 on the ellipse  will subtend a right angle at


The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is a/an


, then PF1 + PF2 equals