A Rectangular Hyperbola Passes Through The Points A(1, 1), B(1, 5), And C(3, 1). The Equation Of Normal To The Hyperbola At A(1, 1) Is

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A rectangular hyperbola passes through the points A(1, 1), B(1, 5), and C(3, 1). The equation of normal to the hyperbola at A(1, 1) is


Correct option is

2x + y = 3

Normal at A is parallel to BC ⇒ equation of normal at A is

                  2x + y = 3



The equation of the tangents to the conic 3x2 – y2 = 3 perpendicular to the line x + 3y = 2 is


If P is a point on the hyperbola 16x– 9y2 = 144 whose foci are S1 andS2, then PS1 – PS2 =


The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is


The locus of the point of intersection of the lines (x + y)t = a and x – y = at, where t is the parameter, is 


If PQ is a double ordinate of the hyperbola  such that OPQ is an equilateral triangle, O being the center of the hyperbola. Then the eccentricity e of the hyperbola satisfies


Portion of asymptote of hyperbola  (between center and the tangent at vertex) in the first quadrant is cut by the line

+ λ (x – a) = 0 (λ is a parameter) then


If a variable line , which is a chord of the hyperbola  (b > a), subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is


If values of m for which the line  touches the hyperbola 16x2 – 9y= 144 are the roots of the equation 

x2 – (a + b)x – 4 = 0, then value of (a, b) is equal to


Let any double ordinate PNP’ of the hyperbola  be produced both sides to meet the asymptotes in Q and Q’, then PQP’Q is equal to


The equation of the line of latum of the rectangular hyperbola xy = c2 is