The circle `x^2+y^2=a^2` cuts off an intercept on the straight line `lx+my=1` which subtends an angle of `45^@` at the origin. Show that `a^2(l^2+m^2)=4-2sqrt2.`

If the striaht line lx+my=1 is a normal to the parbaola y^(2)=4ax then show that, al^(3)+2alm^(2)=m^(2)

The curve x^(2)+y^(2)+2gx+2fy+c=0 intercepts on the line lx+my=1, a length which subtends a right angle at origin then (lg+mf+1)/(l^(2)+m^(2))=

If the straight line lx+my+n=0 touches the : circle x^(2)+y^(2)=a^(2) , show that a^(2)(l^(2)+m^(2))=n^(2)

An equation of a circle through the origin, making an intercept of sqrt(10) on the line y = 2x + (5)/(sqrt(2)) , which subtends an angle of 45^(@) at the origin is

An equation of a cirlce through the origin, making an intercept of sqrt(10) on the line y = 2x + (5)/(sqrt(2)) , which substends an angle of 45^(@) at the origin is

If the line segment on lx+my=n^(2) intercepted by the curve y^(2)=ax subtends a right angle at the origin,then

If the segment intercepted by the parabola y^(2)=4ax with the line lx+my+n=0 subtends a right angle at the vertex then:

If the straight line lx + my = 1 is a normal to ellipse a^2/l^2 + b^2/m^2 is

If the straight line Ix+my+n=0 touches the:(i) circle x^(2)+y^(2)=a^(2), show that a^(2)(l^(2)+m^(2))=n^(2)