If the circles `x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0` and `2x^2+2y^2+2a x+2b y+c=0` intersect othrogonally, then prove that `a a^(prime)`+`b``b``prime=c+c^(prime)/2dot`

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x^2+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

The two lines a x+b y=c and a^(prime) x+b^(prime) y=c^(') are perpendicular if

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

Fid the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d ' are perpendicular.