Family of Straight Lines

Q.

The circle$x^2+y^2=5$ meets the parabola $y^2=4x$ at $P$and$Q$. Then the length $PQ$ is equal to

Q. Locus of the image of the point (2, 3) in the line $(2x-3y+4)+k(x-2y+3)=0,kϵR,$ is a

1. Straight line parallel to x-axis
2. Straight line parallel to y-axis
3. Circle of radius $\sqrt{2}$
4. Circle of adius 3

Q. The difference of the slope of line $3x^2-8xy-3y^2=0$ is

1. $\frac{10}{3}$
2. $\frac{-3}{10}$
3. $\frac{-10}{3}$
4. $\frac{3}{10}$

Q.

If two of the lines given by $3x^3+3x^{2}y-3x{y}^2+d{y}^3=0$ are at right angles then the slope of one of them is

1. -1

2. 1

3. 3

4. -3

Q.

If two of the lines given by $3x^3+3x^{2}y-3x{y}^2+d{y}^3=0$ are at right angles then the slope of one of them is

1. -1

2. 1

3. 3

4. -3

Q. If OP=21 and d.c.'s of $\overrightarrow{OP}$ are $\left(\frac{2}{7},\frac{6}{7},-\frac{3}{7}\right)$, then find the co-ordinates of P.

Q. Let a and b be non-zero and real numbers. Then, the equation
$(a{x}^2+b{y}^2+c)(x^2-5xy+6y^2)=0$ represents

1. Four straight lines, when c=0 and a, b are of the same sign
2. Two straight lines and a circle, when a=b and c is of sign opposite to that of a
3. Two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
4. A circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

Q. In the figure, a square inscribed in a circle with centre O and radius $r$. The area of the region which is not included in the square is ______

1. $\pi (r^2-2)$
2. ${\pi }^2-8r$
3. $r^2(\pi -2)$
4. $2r(2-\pi )$

Q. If the line $y=mx$ bisects the angle between the line $a{x}^2+2hxy+b{y}^2=0$ then $m$ is a root of the quadratic equation: