The ends of hypotenuse of a right angled triangle are (a,0),(-a,0) then the locus of third vertex is
a) `x^(2)-y^(2)=a^(2)`
b) `x^(2)+y^(2)=a^(2)`
c)`x^(2)+y^(2)+a^(2)=0`
d)`x^(2)-y^(2)+a^(2)=0`

The ends of hypotenuse of a right angled triangle are (5,0),(-5,0) and the locus of third vertex is lx^(2)+my^(2)=25 then l+m=

If x=10 and y=0.1, which of the following is the greatest? x^(2)+y^(2)( b) x^(2)-y^(2)( c) x^(2)backslash y^(2) (d) (x^(2))/(y^(2))

Let the foci of the ellipse (x^(2))/(9)+y^(2)=1 subtend a right angle at a point P. Then,the locus of P is (A) x^(2)+y^(2)=1(B)x^(2)+y^(2)=2 (C) x^(2)+y^(2)=4(D)x^(2)+y^(2)=8

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola xy=c^(2) is (A)(x^(2)-y^(2))^(2)+4c^(2)xy=0(B)(x^(2)+y^(2))^(2)+4c2^(x)y=0(C)x^(2)-y^(2))^(2)+4c2^(x)y=0(C)x^(2)-y^(2))^(2)+4cxy=0(D)(x^(2)+y^(2))^(2)+4cxy=0

Let vertices of the triangle ABC is A(0,0),B(0,1) and C(x,y) and perimeter is 4 then the locus of C is : (A)9x^(2)+8y^(2)+8y=16(B)8x^(2)+9y^(2)+9y=16(C)9x^(2)+9y^(2)+9y=16(D)8x^(2)+9y^(2)-9x=16

If points A and B are (1,0) and (0,1) respectively,and point C is on the circle x^(2)+y^(2)=1, then the locus of the orthocentre of triangle ABC is x^(2)+y^(2)=4x^(2)+y^(2)-x-y=0x^(2)+y^(2)-2x-2y+1=0x^(2)+y^(2)+2x-2y+1=0

From the points (3,4), chords are drawn to the circle x^(2)+y^(2)-4x=0 .The locus of the midpoints of the chords is (a) x^(2)+y^(2)-5x-4y+6=0(b)x^(2)+y^(2)+5x-4y+6=0(c)x^(2)+y^(2)-5x+4y+6=0(d)x^(2)+y^(2)-5x-4y-6=0

If the lines 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of circumference 10 pi ,then the equation of the circle is (A) x^(2)+y^(2)-2x+2y-23=0 (B) x^(2)+y^(2)+2x-2y-23=0 (C) x^(2)+y^(2)+2x+2y-23=0 (D) x^(2)+y^(2)-2x-2y-23=0

A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n dm vary subject to the condition l^2+m^2=1, then the locus of its circumcenter is (a) (x^2-y^2)^2=x^2+y^2 (b) (x^2+y^2)^2=(x^2-y^2) (c) (x^2+y^2)^2=4x^2y^2 (d) (x^2-y^2)^2=(x^2+y^2)^2

In triangle ABC ,the equation of side BC is x-y=0. The circumcenter and orthocentre of triangle are (2,3) and (5,8), respectively. The equation of the circumcirle of the triangle is x^(2)+y^(2)-4x+6y-27=0x^(2)+y^(2)-4x-6y-27=0x^(2)+y^(2)+4x+6y-27=0x^(2)+y^(2)+4x+6y-27=0