Tangents are drawn to the hyperbola 9x2−4y2=1 parallet to the sraight line 2x−y=1. The points of contact of the tangents on the hyperbola are (A) (222,21) (B) (−229,21) (C) (33,−22) (D) (−33,22)
Statement 1 : If (3, 4) is a point on a hyperbola having foci (3, 0) and (λ,0) , the length of the transverse axis being 1 unit, then λ can take the value 0 or 3. Statement 2 : ∣∣SprimeP−SP∣∣=2a, where SandS′ are the two foci, 2a is the length of the transverse axis, and P is any point on the hyperbola.
Find the equation of the hyperbola which has 3x−4y+7=0 and 4x+3y+1=0 as its asymptotes and which passes through the origin.
If the vertex of a hyperbola bisects the distance between its center and the correspoinding focus, then the ratio of the square of its conjugate axis to the square of its transverse axis is 2 (b) 4 (c) 6 (d) 3
The distance between two directrices of a rectangular hyperbola is 10 units. Find the distance between its foci.
If the distance between two parallel tangents having slope m drawn to the hyperbola 9x2−49y2=1 is 2, then the value of 2∣m∣ is_____
The chord PQ of the rectangular hyperbola xy=a2 meets the axis of x at A;C is the midpoint of PQ; and O is the origin. Then ΔACO is equilateral (b) isosceles right-angled (d) right isosceles
Let aandb be nonzero real numbers. Then the equation (ax2+by2+c)(x2−5xy+6y2)=0 represents. four straight lines, when c=0 and a,b are of the same sign. two straight lines and a circle, when a=b and c is of sign opposite to that a two straight lines and a hyperbola, when aandb are of the same sign and c is of sign opposite to that of a a circle and an ellipse, when aandb are of the same sign and c is of sign opposite to that of a