The intercepts of a straight line upon the coordinate axes are a and b . If the length of the perpendicular on this line from the origin be p, prove that `(1)/(a^(2))+(1)/(b^(2))=(1)/(p^(2))`.

if P is the length of perpendicular from origin to the line x/a+y/b=1 then prove that 1/(a^2)+1/(b^2)=1/(p^2)

Find the coordinates of the foot of the perpendicular drawn from the point (2,-5) on the straight line x=y+1.

If p is the length of the perpendicular from the origin on the line whose intercepts on the axes are a and b, then-

In the right-angled triangle ABC, /_C = 90^(@) .If the length of perpendicular drawn from C on AB be p and AB=c,BC =a,CA=b , then prove that (a)(1)/(p^(2))=(1)/(a^(2) )+ (1)/(b^(2)) , (b) pc = ab .

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B and C. Show that the locus of the centroid of the tetrahedron OABC is (1)/(x^2)+(1)/(y^2)+(1)/(z^2)=(16)/(p^2) .

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/p^(2) = 1/a^(2) + 1/b^(2) .

Find the slope and y intercept of the straight line 2x-3y+5=0 . Also find the length of the portion of the line intercepted between the coordinate axes.

If length of focal chord P Q is l , and p is the perpendicular distance of P Q from the vertex of the parabola, then prove that lprop1/(p^2)dot

The coordinates of the foot of the perpendicular drawn from the origin upon a line are (h,k) , show that the equation of the line is hx+ky=h^(2)+k^(2)(h^(2)+k^(2)ne0) .

The line x/a-y/b=1 cuts the x-axis at P. Find the equation of the line through p and perpendicular to the given line.