Question

The equation of the conic with focus at (1, –1), directrix along – y + 1 = 0 and with eccentricity  is

Solution

Correct option is

2xy – 4x + 4y + 1 = 0

 

S(1, –1) = focus, directrix is (x – y + 1) = 0                   …… (1)

P(x, y) is any point on the curve and 

Curve is hyperbola

         PS = ePM

Length of ⊥ from P on (x – y + 1) = 0                  

Solve to get –4x + 4y + 2yx + 1 = 0

SIMILAR QUESTIONS

Q1

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Q2

Let P and , where , be two points on the hyperbola . If (h, k) is the point of intersection of the normal’s at P and Q, then k is equal to

Q3

If x = 9 is the chord of contact of the hyperbola x2 – y= 9, then equation of corresponding of tangents is

Q4

The locus of the mid-point of the chord of the circle x2 + y= 16, which are tangent to the hyperbola 9x2 – 16y= 144 is

Q5

The angle between lines joining origin to the points of intersection of the line  and the curve y2 – x2 = 4 is

Q6

If a circle cuts a rectangular hyperbola xy = c2 in A, B, C, D and the parameters of these four points be t1t2t3 and t4 respectively. Then

Q7

The locus of the middle point of the chords of hyperbola 3x2 – 2y2 + 4x – 6y = 0 parallel to y = 2x is

Q8

The angle between the asymptotes of the hyperbola  is

Q9

If P is any point on the hyperbola , and Sand S2 are its foci, then | S1P – S2| =

Q10

The point of intersection of two perpendicular tangents to  lies on the circle