Find the equation of the circle, the coordinates of the end points of one of whose diameters are (i) ` A (3, 2 ) and B(2, 5)` (ii) `A (5, - 3) and B(2, - 4 )` (iii) ` A(-2, -3) and B(-3, 5)` (iv) `A(p, q), B (r, s )`

Find the equation of the circle, the coordinates of the end points of

1.	Find the equation of the circle, the coordinates of the end points of one of whose diameters are (i) ` A (3, 2 ) and B(2, 5)` (ii) `A (5, - 3) and B(2, - 4 )` (iii) ` A(-2, -3) and B(-3, 5)` (iv) `A(p, q), B (r, s )`
Answer» Correct Answer - (i) ` x ^(2) + y ^(2) - 5x - 7y + 16 = 0` (ii) ` x ^(2 ) + y ^(2) - 7x + 7y + 22 = 0` (iii) ` x ^(2) + y ^(2) + 5x - 2y - 9 = 0` (iv) ` (x - p) (x - r) + (y - q ) (y - s ) = 0 `

Discussion

No Comment Found

Related InterviewSolutions

The loucs of the centre of the circle which cuts orthogonally the circle `x^(2)+y^(2)-20x+4=0` and which touches x=2 isA. `x^(2)=16y`B. `x^(2)=16y+4`C. `y^(2)=16x`D. `y^(2)=16x+4`
If a variable line, `3x + 4y -lambda = 0` is such that the two circles `x^(2)+y^(2)-2x-2y+1=0` and `x^(2)+y^(2)-18x-2y+78=0` are not its opposite sides, then the set of all values of `lambda` is the intervalA. [13, 23]B. [2,17]C. [12,21]D. [23,31]
The equation of a circle which cuts the three circles `x^(2)+y^(2)+2x+4y+1=0,x^(2)+y^(2)-x-4y+8=0` and `x^(2)+y^(2)+2x-6y+9=0` orthogonlly isA. `x^(2)+y^(2)-2x-4y+1=0`B. `x^(2)+y^(2)+2x+4y+1=0`C. `x^(2)+y^(2)-2x+4y+1=0`D. `x^(2)+y^(2)-2x-4y-1=0`
Two variable chords AB and BC of a circle `x^(2)+y^(2)=a^(2)` are such that `AB=BC=a`. M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C isA. `x^(2)+y^(2)=a^(2)`B. `x^(2)+y^(2)=2a^(2)`C. `x^(2)+y^(2)=4a^(2)`D. `x^(2)+y^(2)=8a^(2)`
One of the limiting points of the co-axial system of circles containing the circles `x^(2)+y^(2)-4=0andx^(2)+y^(2)-x-y=0` isA. `(sqrt2,sqrt2)`B. `(-sqrt2,sqrt2)`C. `(-sqrt2-sqrt2)`D. None of these
The limiting points of the system of circles represented by the equation `2(x^(2)+y^(2))+lambda x+(9)/(2)=0`, areA. `(pm(3)/(2),0)`B. `(0,0)and((9)/(2),0)`C. `(pm(9)/(2),0)`D. `(pm3,0)`
`t_(1),t_(2),t_(3)` are lengths of tangents drawn from a point (h,k) to the circles `x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0` respectively further, `t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16`. Locus of the point (h,k) consist of a straight line `L_(1)` and a circle `C_(1)` passing through origin. A circle `C_(2)` , which is equal to circle `C_(1)` is drawn touching the line `L_(1)` and the circle `C_(1)` externally. Equation of `L_(1)` isA. x+y=0B. x-y=0C. 2x+y=0D. x+2y=0
Find the equation of the radical axis of circles `x^2+y^2+x-y+2=0` and `3x^2+3y^2-4x-12=0`A. `2x^(2)+2y^(2)-5x+y-14=0`B. `7x-3y+18=0`C. `5x-y+14=0`D. None of these
Find the equation of radical axis of the circles `x^(2)+y^(2)-3x+5y-7=0` and `2x^(2)+2y^(2)-4x+8y-13=0`.
The radius centre of the circles `x^(2)+y^(2)=1,x^(2)+y^(2)+10y+24=0andx^(2)+y^(2)-8x+15=0` isA. (2,5/2)B. (-2,5/2)C. (-2,-5/2)D. (2,-5/2)

Find the equation of the circle, the coordinates of the end points of one of whose diameters are (i) ` A (3, 2 ) and B(2, 5)` (ii) `A (5, - 3) and B(2, - 4 )` (iii) ` A(-2, -3) and B(-3, 5)` (iv) `A(p, q), B (r, s )`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment