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




None of these
easy
Solution
The point A(4, 2) lies on 3x – 5y = 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 A which lies on the line. It is easy to find that
SIMILAR QUESTIONS
Equation of tangent to the hyperbola 2x^{2} – 3y^{2} = 6 which is parallel to the line y = 3x + 4 is
Let , be two points on the hyperbola . If (h, k) is thepoint of intersection of the normal’s at P and Q, k is equal to
Let , be two points on the hyperbola . If (h, k) is thepoint of intersection of the normal’s at P and Q, k is equal to
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
If x = 9 is the chord of contact of the hyperbola x^{2} – y^{2} = 9, then the equation of the corresponding pair of triangle is.
Find the equations of tangents to the hyperbola x^{2} – 4y = 36 which are perpendicular to the line x – y + 4 = 0
Find the coordinates of foci, the eccentricity and latus rectum. Determine also the equation of its directrices for the hyperbola
4x^{2} – 9y^{2} =36.
The asymptotes of the hyperbola makes an angle 60^{0} with xaxis. Write down the equation of determiner conjugate to the diameter y = 2x.
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.
Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2x^{2} – 3y^{2} = 6.