Home
Class 12
MATHS
If the system of equations ax+hy+g=0 …...

If the system of equations
ax+hy+g=0 ….(i)
hx+by+f=0…(ii)
and `ax^2+2hxy+by^2 + 2gx+ 2fy+c+t=0`….(iii)
has a unique solution and `(abc+2fgh-af^2-bg^2-ch^2)/(h^2-ab)=8` , find the value of 't'.

Text Solution

Verified by Experts

The correct Answer is:
8
Promotional Banner

Similar Questions

Explore conceptually related problems

ax^2+2hxy+by^2+2gx+2fy+c=0

The equations a^2x^2+2h(a+b)xy+b^2y^2=0 and ax^2+2hxy+by^2=0 represent.

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

If the equation ax^2 +2hxy + by^2 = 0 and bx^2 - 2hxy + ay^2 =0 represent the same curve, then show that a+b=0 .

If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis,then prove that 2fgh=bg^(2)+ch^(2)

The principal axes of the hyperbola ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 are parallel to the lines

The equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a circle if

If the centre of the hyperbola whose equation is ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 " be " (alpha, beta) , then find the equation of the asymptotes.

Derive a method to find separate equation of pair of lines given by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0