The equation of the circle passing through (1, 5) and (4, 1) and touching y-axis is x² + y² − 5x − 6y + 9 + \(\lambda\)(4x + 3y − 19) = 0 where λ is equal to

(a)

\(0,-\frac { 40 }{ 9 } \)

(b)

0

(c)

\(\frac { 40 }{ 9 } \)

(d)

\(\frac { -40 }{ 9 } \)

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

(a)

\(\frac { 4 }{ 3 } \)

(b)

\(\frac { 4 }{ \sqrt { 3 } } \)

(c)

\(\frac { 2 }{ \sqrt { 3 } } \)

(d)

\(\frac { 3 }{ 2 } \)

If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3, 0) and F₂ (-3, 0) then PF₁  + PF₂ is

(a)

8

(b)

6

(c)

10

(d)

12

The radius of the circle passing through the point(6, 2) two of whose diameter are x + y = 6 and x + 2y = 4 is

(a)

10

(b)

\( {2} \sqrt {5}\)

(c)

6

(d)

4

The area of quadrilateral formed with foci of the hyperbolas \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \text { and } \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=-1\)

(a)

4(a²+b²)

(b)

2(a²+b²)

(c)

a² +b²

(d)

\(\frac { 1 }{ 2 } \)(a²+b²)