Equation of Circle Whose Extremities of a Diameter Given
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Q.
An isosceles right angled triangle is inscribed in the circle x2+y2=r2. If the coordinates of an end of the hypotenuse are (a, b), the coordinates of the vertex are
(-a, -b)
(b, -a)
(b, a)
(-b, -a)
Q. The intercept on the line y = x by the circle x2+y2−2x=0 is AB. The equation of the circle on AB as a diameter is
- x2+y2+x+y=0
- x2+y2+x−y=0
- x2+y2−x−y=0
- x2+y2−x+y=0
Q. In the ΔABC, the co-ordinate of B are (0, 0), AB=2, ∠ABC=π3 and middle point of BC has the co-ordinates (2, 0). The coordinates of point A of the triangle is
- (53, 1√3)
- (4+√33, 12)
- (1, √3)
- (12, √32)
Q. Let P(x1, y1) and Q(x2, y2) are two points such that their abscissa x1 and x2 are the roots of the equation x2+2x−3=0 while the ordinates y1 and y2 are the roots of the equation y2+4y−12=0. The centre of the circle with PQ as diameter is
- (-1, -2)
- (1, 2)
- (1, -2)
- (-1, 2)
Q. The radius of the circle which touches y−axis at (0, 0) and passes through the point (b, c) is:
- b2+c22|b|
- b2+c22|c|
- b2+c22
- |b|2(b2+c2)
Q. If a circle with radius 2 units touches the x-axis at (1, 0) then its center may be:
- (±1, 2)
- (±1, ±2)
- (1, ±2)
- (1, ±√5)