Find the locus of P, if for all values of \(\alpha\) the co-ordinates of a moving point P is  (9 cos \(\alpha\) 9 sin \(\alpha\))

Find the equation of the lines passing through the point (1, 1) 
(i) with y-intercept (-4)
(ii) with slope 3
(iii) and (-2, 3)
(iv) and the perpendicular from the origin makes an angle 60° with x- axis.

Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y - 15 = 0 are paralle llines.

Find the equation of the straight line parallel to 5x - 4y + 3 = 0 and having x-intercept 3.

Determine the equation of line through the point (-4, -3) and perpendicular to y-axis.

If p (r, c) is mid - point of a line segment between the axes, then show that \(\frac{x}{r}+\frac{y}{c}=2\)

Find the equation of the straight line on which the length of the perpendicular from the origin is 4 units and the line makes an angle of 120° with positive direction of x-axis.

Find the value of a and p if the equation x-cos a + y sin a = p is the normal form of the line \(\sqrt{3x}+y+2=0\)

A straight line is drawn through the point p(2, 3) and is inclined at an angle of 30° with x-axis. Find the co-ordinates of two points on it at a distance of 4 from P on either side of P.

If p is the length of the perpendicular from the origin to the line \(\frac{x}{a}+\frac{y}{b}=1\), then prove that \(\frac{1}{p_2}=\frac{1}{a^2}+\frac{1}{b^2}\)