Home
Class 12
MATHS
The abscissa of A and B are the roots of...

The abscissa of A and B are the roots of the equation `x^(2) + 2ax -b^(2) =0` and their ordinates are the roots of the equation `y^(2) + 2py -q^(2) = 0.` The equation of the circle with AB as diameter is

A

`x^(2)+y^(2)+2ax+2py-b^(2)-q^(2)=0`

B

`x^(2)+y^(2)+2ax+2py+b^(2)-q^(2)=0`

C

`x^(2)+y^(2)-2qx-2py+b^(2)+q^(2)=0`

D

`x^(2)+y^(2)+2ax-2py+b^(2)-q^(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

The abscisae of A and B are the roots of the equation x ^(2) + 2ax -b ^(2) =0 and their ordinates are the roots of the equation y ^(2) + 2 py -q ^(2) =0. The equation of the circle with AB as diameter is

The abscissa of the two points A and B are the roots of the equation x^2+2a x-b^2=0 and their ordinates are the roots of the equation x^2+2p x-q^2=0. Find the equation of the circle with AB as diameter. Also, find its radius.

The abscissa of the two points A and B are the roots of the equation x^2+2a x-b^2=0 and their ordinates are the roots of the equation x^2+2p x-q^2=0. Find the equation of the circle with AB as diameter. Also, find its radius.

STATEMENT-1 : The area of equilateral triangle inscribed in the circle x^(2) + y^(2) + 6x + 8y + 24 = 0 is (3sqrt(3))/(4) . STATEMENT-2 : The abscissae of two points A and B are the roots of the equation x^(2) + 3ax + b^(2) =0 and their ordinates are the roots of x^(2) + 3bx + a^(2) =0 Then the equation of the circle with AB as diameter is x^(2) + y^(2) + 3ax + 3by + a^(2) + b^(2) = 0 . STATEMENT-3 : If the circle x^(2) + y^(2) + 2gx + 2fx +c =0 always passes through exactly three quadrants not passing through origin then c gt 0 .

The abscissae of two points A and B are the roots of the equaiton x^2 + 2x-a^2 =0 and the ordinats are the roots of the equaiton y^2 + 4y-b^2 =0 . Find the equation of the circle with AB as its diameter. Also find the coordinates of the centre and the length of the radius of the circle.

The roots of the equation x^(2)+2ax+a^(2)+b^(2)=0 are

The roots of the equation x^2+ax+b=0 are

If the abscissae of points A, B are the roots of the equation, x^(2) + 2ax - b^(2) = 0 and ordinates of A, B are roots of y^(2)+2py- q^(2) = 0 , then find the equation of a circle for which overline(AB) is a diameter.

Find the roots of the equations. Q. x^(2)-2x+5=0

Find the roots of the equations. Q. 2x^(2)+x-3=0