The area of the circle centred at (1, 2) and passing through (4, 6) is
5π
10π
25π
none of these
Equation of a circle which passes through (3, 6) and touches the axes is
x² + y² + 6x + 6y + 3 = 0
x² + y² − 6x − 6y − 9 = 0
x² + y² − 6x − 6y = 0
none of these
Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) is
x² + y² + 13y = 0
3x² + 3y² + 13x + 3 = 0
6x² + 6y² − 13x = 0
x² + y² + 13x + 3 = 0
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is
x² + y² = 9a²
x² + y² = 16a²
x² + y² = 4a²
x² + y² = a²
If the focus of a parabola is (0, −3) and its directrix is y = 3, then its equation is
x² = −12y
x² = 12y
y² = −12x
y² = 12x
If the parabola y² = 4ax passes through the point (3, 2), then the length of its latus rectum is
2/3
4/3
1/3
4
If the vertex of the parabola is the point (−3, 0) and the directrix is the line x + 5 = 0, then its equation is
y² = 8(x + 3)
x² = 8(y + 3)
y² = −8(x + 3)
y² = 8(x + 5)
The equation of the ellipse whose focus is (1, −1), the directrix the line x − y − 3 = 0 and eccentricity \(\dfrac{1}{2}\) is
7x² + 2xy + 7y² − 10x + 10y + 7 = 0
7x² + 2xy + 7y² + 7 = 0
7x² + 2xy + 7y² + 10x − 10y − 7 = 0
none
The length of the latus rectum of the ellipse 3x² + y² = 12 is
4
3
8
4/√3
If e is the eccentricity of the ellipse \(\dfrac{x²}{a²} + \dfrac{y²}{b²} = 1\) (a < b), then
b² = a²(1 − e²)
a² = b²(1 − e²)
a² = b²(e² − 1)
b² = a²(e² − 1)
The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half of the distance between the foci is
4/3
4/√3
2/√3
none of these
The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt{2}\). Its equation is
x² − y² = 32
x²/4 − y²/9 = 1
2x − 3y² = 7
none of these
Equation of the hyperbola with eccentricity \(\dfrac{3}{2}\) and foci at (±2, 0) is
x²/4 − y²/5 = 4/9
x²/9 − y²/9 = 4/9
x²/4 − y²/9 = 1
none of these