Which of the following equation is the locus of (at², 2at)

(a)

\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)

(b)

\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

(c)

x² + y² = a²

(d)

y² = 4ax

The slope of the line which makes an angle 45^o with the line 3x- y = -5 are:

(a)

1, -1

(b)

\(\frac{1}{2},-2\)

(c)

\(1,\frac{1}{2}\)

(d)

\(2,-\frac{1}{2}\)

The coordinates of the four vertices of a quadrilateral are (-2, 4), (-1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (-1, 2) and dividing the quadrilateral in the equal areas is

(a)

x + 1 = 0

(b)

x + y = 1

(c)

x + y + 3 = 0

(d)

x - y + 3 = 0

Equation of the straight line perpendicular to the line x - y + 5 = 0, through the point of intersection the y-axis and the given line

(a)

x - y - 5 = 0

(b)

x + y - 5 = 0

(c)

x + y + 5 = 0

(d)

x + y + 10 = 0

The line (p + 2q)x + (p - 3q)y = p - q for different values of p and q passes through the point

(a)

\(\left(\frac{3}{5},\frac{5}{2}\right)\)

(b)

\(\left(\frac{2}{5},\frac{2}{5}\right)\)

(c)

\(\left(\frac{3}{5},\frac{3}{5}\right)\)

(d)

\(\left(\frac{2}{5},\frac{3}{5}\right)\)

The distance between the line 12x - 5y + 9 = 0 and the point (2, 1) is ______________

(a)

\(\pm\frac{28}{13}\)

(b)

\(\frac{28}{13}\)

(c)

\(-\frac{28}{13}\)

(d)

none of these

The inclination to the x-axis and intercept on y-axis of the line \(\sqrt {2y}=x+2\sqrt 2\) ______________

(a)

\(30^0,\sqrt 2\)

(b)

30⁰,2

(c)

\(45^0,2\sqrt 2\)

(d)

45⁰,2

The equation of a line which makes an angle of 135° with positive direction of x-axis and passes through the point (1, 1) is ______________

(a)

x+y=2

(b)

x-y=0

(c)

\(2\sqrt {2x}-\sqrt {2y}=0\)

(d)

x-3y=0

The lines x cos \(\alpha\) + y sin \(\alpha\) = p and xcos\(\beta\) + y sin\(\beta\) = q will be perpendicular if ______________

(a)

\(\alpha =\beta\)

(b)

\(\alpha-\beta=\frac{\pi}{2}\)

(c)

\(|\alpha-\beta|=\frac{\pi}{2}\)

(d)

\(\alpha-\beta=0\)

The image of the point (1, 2) with respect to the line y = x is ______________

(a)

(-1, -2)

(b)

(2, 1)

(c)

(2, -1)

(d)

(2, 1)