The length of the chord of the ellipse x24+ y22=1, whose mid-point is (1, 12 ), is :
(1) 23 15
Chord with mid-point (1, 12 ): T=S1 x4+ y4= 38 x+y= 32 (slope -1).
[figure]
Put y= 32-x in x2+2y2=4: 6x2-12x+1=0 (x1-x2)2=4- 23= 103
Slope -1 PQ= 2 |x1-x2|= 203= 23 15
Answer: (1)
Let the shortest distance from (a,0), a>0, to the parabola y2=4x be 4. Then the equation of the circle passing through the point (a,0) and the focus of the parabola, and having its centre on the axis of the parabola is :
The focus of the parabola y2=4x+16 is the centre of the circle C of radius 5. If the values of , for which C passes through the point of intersection of the lines 3x-y=0 and x+ y=4, are 1 and 2, 1< 2, then 12 1+29 2 is equal to .
Let the foci of a hyperbola be (1,14) and (1,-12). If it passes through the point (1,6), then the length of its latus-rectum is :
A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2,5) and intersects the circle C at exactly two points. If the set of all possible values of r is the interval ( , ), then 3 -2 is equal to :
Let the parabola y=x2+px-3, meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1,-1) passes through the points P, Q and R, then the area of PQR is :
Let P(4,4 3) be a point on the parabola y2=4ax and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :
Let E: x2a2+ y2b2=1, a>b and H: x2A2- y2B2=1. Let the distance between the foci of E and the foci of H be 2 3. If a-A=2, and the ratio of the eccentricities of E and H is 13, then the sum of the lengths of their latus rectums is equal to :