If the point Q is choosen such that PA, PQ and PB are in G.P, then locus of point Q is `x y-y+2x-c^2=0` (b) `x y+y-2x+c^2=0` `x y+y+2x+c^2=0` (d) `x y-y-2x-c^2=0`

Comprehension (Q.6 to 8) A line is drawn through the point P(-1,2) meets the hyperbola x y=c^2 at the points A and B (Points A and B lie on the same side of P) and Q is a point on the lien segment AB. If the point Q is choosen such that PQ, PQ and PB are inAP, then locus of point Q is x+y(1+2x) (b) x=y(1+x) 2x=y(1+2x) (d) 2x=y(1+x)

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Image of the locus of R in the line y = - x is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Locus of R is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x - 4y=0 (D) x^2 + y^2 + 2x - 4y = 0

The equation of the normal to the curve y=x(2-x) at the point (2,\ 0) is x-2y=2 (b) x-2y+2=0 (c) 2x+y=4 (d) 2x+y-4=0

The point of intersection of the tangents of the parabola y^(2)=4x drawn at the endpoints of the chord x+y=2 lies on (a)x-2y=0 (b) x+2y=0( c) y-x=0 (d) x+y=0

From the point A (0, 3) on the circle x^2+4x+(y-3)^2=0 a chord AB is drawn & extended to a M point such that AM=2AB. The equation of the locus of M is: (A)x^2 +8x+y^2 =0 (B)x^2+8x+(y-3)^2=0 (C)(x-3)^2+8x+y^2=0 (D)x^2+8x+8y^=0

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The locus of the midpoint of PQ is y^(2)+4x+2=0y^(2)-4x+2=0x^(2)-4y+2=0x^(2)+4y+2=0

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

Find the equation of the tangent line to the curve y=(3x^2-1)/x at the point (1,2) is (a) 4x-y-1=0 (b) 4x+y+2=0 (c)x-y-1=0 (d) 4x-y-2=0

The locus of the mid-point of a chord of the circle x^2 + y^2 -2x - 2y - 23=0 , of length 8 units is : (A) x^2 + y^2 - x - y + 1 =0 (B) x^2 + y^2 - 2x - 2y - 7 = 0 (C) x^2 + y^2 - 2x - 2y + 1 = 0 (D) x^2 + y^2 + 2x + 2y + 5 = 0