HARD
Earn 100

Find equations of the tangents drawn from (4,-3) to hyperbola x216-y29=-1.

Important Questions on Conic sections

MEDIUM
A tangent drawn to hyperbola x2a2-y2b2=1 at Pπ6 forms a triangle of area 3a2 square units, with coordinate axes. If the eccentricity of hyperbola is e, then the value of e2-9 is
HARD
A line parallel to the straight line 2x-y=0 is tangent to the hyperbola x24y22=1 at the point x1, y1. Then x12+5y12 is equal to
HARD
Let a and b be positive real numbers such that a>1 and b<a. Let P be a point in the first quadrant that lies on the hyperbola x2a2-y2b2=1. Suppose the tangent to the hyperbola at P passes through the point 1,0, and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let Δ denote the area of the triangle formed by the tangent at P, the normal at P and the x -axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?
EASY
The equation of a tangent to the hyperbola, 4x2-5y2=20, parallel to the line x-y=2, is
HARD
Consider the hyperbola H:x2-y2=1 and a circle S with center Nx2,0. Suppose that H and S touch each other at point Px1,y1 with x1>1 & y1>0. The common tangent to H and S at P intersects the x-axis at point M. If l,m is the centroid of the triangle ΔPMN, then the correct expression(s) is (are)
HARD
Equation of a tangent to the hyperbola 5x2-y2=5 and which passes through an external point (2, 8) is
HARD
If the line y=m x+c is a common tangent to the hyperbola x2100-y264=1 and the circle x2+y2=36, then which one of the following is true?
HARD
The total number of points on the curve x2-4y2=1 at which the tangents to the curves are parallel to the line x=2y is
HARD
If 2x-y+1=0 is a tangent to the hyperbola x2a2-y216=1 , then which of the following CANNOT be sides of a right angled triangle?
EASY
If the eccentricity of the standard hyperbola passing through the point (4,6) is 2, then the equation of the tangent to the hyperbola at (4,6) is:
EASY
The straight line x+y=2p will touch the hyperbola 4x2-9y2=36 if
MEDIUM
A hyperbola passes through the point P2,3 and has foci at ± 2,0. Then the tangent to this hyperbola at P also passes through the point
EASY
Consider a hyperbola H : x2-2y2=4. Let the tangent at a point P(4,6) meet the x-axis at Q and latus rectum at Rx1,y1,x1>0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR (in sq. units) is equal to
MEDIUM
The distance between the tangents to the hyperbola x220-3y24=1 which are parallel to the line x+3y=7 is
MEDIUM
The locus of the midpoints of the chord of the circle, x2+y2=25 which is tangent to the hyperbola, x29-y216=1 is :
MEDIUM
The point P(-26,3) lies on the hyperbola x2a2-y2 b2=1 having eccentricity 52. If the tangent and normal at $P$ to the hyperbola intersect its conjugate axis at the points Q and R respectively, then QR is equal to:
HARD
Let a line L:2x+y=k, k>0 be a tangent to the hyperbola x2-y2=3. If L is also a tangent to the parabola y2=αx, then α is equal to:
EASY
Let P be the point of intersection of the common tangents to the parabola y2=12x and the hyperbola  8x2-y2=8. If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio:
EASY

The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola x 2 4 - y 2 5 = 1 , meets the x-axis and y-axis at A and B, respectively. Then OA2-OB2, where O is the origin, equals 

EASY
If the line 2x+6y=2 touches the hyperbola x2-2y2=4, then the point of contact is