The image of the pair of lines represented by `a x^2+2h x y+b y^2=0` by the line mirror `y=0` is `a x^2-2h x y-b y^2=0` `b x^2-2h x y+a y^2=0` `b x^2+2h x y+a y^2=0` `a x^2-2h x y+b y^2=0`

Statement 1 : If -2h=a+b , then one line of the pair of lines a x^2+2h x y+b y^2=0 bisects the angle between the coordinate axes in the positive quadrant. Statement 2 : If a x+y(2h+a)=0 is a factor of a x^2+2h x y+b y^2=0, then b+2h+a=0 Both the statements are true but statement 2 is the correct explanation of statement 1. Both the statements are true but statement 2 is not the correct explanation of statement 1. Statement 1 is true and statement 2 is false. Statement 1 is false and statement 2 is true.

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

The equation of the circle through the points of intersection of x y -1 -0, x y -2x-4 y l 0 and touching the line x 2y 0, is (B) x y 2 x+20 (C) x y (D) 2 (x2 y x 2

The equations a^2x^2+2h(a+b)xy+b^2y^2=0 and ax^2+2hxy+by^2=0 represent.

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

The equatioin of the image of the circle x^(2)+y^(2)+016x-24y+183=0 in the line mirror 4x+7y+13=0 is: a.x^(2)+y^(2)+32x-4y+235=0 b.x^(2)+y^(2)+32x-4y-235=0cx^(2)+y^(2)+32x-4y-235=0dx^(2)+y^(2)+32x-4y-235=0dx^(2)+y^(2)+32x+4y+235=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

The equation of the circle passing through (1/2, -1) and having pair of straight lines x^2 - y^2 + 3x + y + 2 = 0 as its two diameters is : (A) 4x^2 + 4y^2 + 12x - 4y - 15 = 0 (B) 4x^2 + 4y^2 + 15x + 4y - 12 = 0 (C) 4x^2 + 4y^2 - 4x + 8y + 5 = 0 (D) none of these

If a+b=2h, then the area of the triangle formed by the lines ax^(2)+2hxy+by^(2)=0 and the line x-y+2=0, in sq.units is

The equation of a circle of radius 1 touching the circles x^2 + y^2 - 2 |x| = 0 is: (A) x^2 + y^2 + 2sqrt(3x) - 2 = 0 (B) x^2 + y^2 - 2sqrt(3)y+2=0 (C) x^2 + y^2 + 2sqrt(3) y + 2 = 0 (D) x^2 + y^2 + 2 sqrt(3) x + 2 = 0