, then PF1 + PF2 equals
This equation represents an ellipse with eccentricity e given by
So, the coordinates of the foci are i.e., (3, 0) and (–3, 0).
Thus, F1 and F2 are the foci of the ellipse.
Since, the sum of the focal distances of a point on an ellipse is equal to its major axis.
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 = r2 (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
The number of values of c such that the straight line y = 4x + ctouches the curve , is
An ellipse slides between two perpendicular straight lines. Then, the locus of its centre is a/an