Question

Find the distance from A(4, 2) to the points in which the line 3x – 5= 2 meets the hyperbola xy = 24. Are these points on the same side of A?

Solution

Correct option is

The point A(4, 2) lies on 3x – 5= 2. It meets the hyperbola in

 and C(–6, –4). If we put these points in the line the results are of opposite sides of the line and hence on opposite sides of point which lies on the line. It is easy to find that 

SIMILAR QUESTIONS

Q1

Equation of tangent to the hyperbola 2x2 – 3y2 = 6 which is parallel to the line y = 3x + 4 is

Q2

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

Q3

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

Q4

Let two perpendicular chords of the ellipse  each passing through exactly one of the foci meet at a point P. If from P two tangents are drawn to the hyperbola , then 

Q5

If x = 9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of triangle is.

Q6

Find the equations of tangents to the hyperbola x2 – 4y = 36 which are perpendicular to the line x – y + 4 = 0

Q7

Find the coordinates of foci, the eccentricity and latus rectum. Determine also the equation of its directrices for the hyperbola

4x2 – 9y2 =36.

Q8

The asymptotes of the hyperbola  makes an angle 600 with x-axis. Write down the equation of determiner conjugate to the diameter y = 2x.

Q9

Two straight lines pass through the fixed points  and have gradients whose product is k > 0. Show that the locus of the points of intersection of the lines is a hyperbola.

Q10

Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2x2 – 3y2 = 6.