If the equation x^2 + y^2 + 2gx + 2fy + 1 = 0 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The general equation of a second-degree curve is given by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $x^2 + y

Vedclass · Accepted Answer

$f^2 + g^2 = 1$

Vedclass · Answer

(A) The general equation of a second-degree curve is given by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $x^2 + y^2 + 2gx + 2fy + 1 = 0$,we get $a = 1, b = 1, h = 0, c = 1$.The condition for this equation to represent a pair of straight lines is $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.Substituting the values: $(1)(1)(1) + 2(f)(g)(0) - (1)(f^2) - (1)(g^2) - (1)(0)^2 = 0$.This simplifies to $1 - f^2 - g^2 = 0$.Therefore,$f^2 + g^2 = 1$.

If the equation $x^2 + y^2 + 2gx + 2fy + 1 = 0$ represents a pair of straight lines,then:

Similar Questions

If the sum of the slopes of the pair of lines represented by $4x^2 + 2hxy - 7y^2 = 0$ is equal to the product of the slopes,then the value of $h$ is

If the lines represented by the equation $4xy + 6x - 8y + c = 0$ form a rectangle with the coordinate axes,then the area of the rectangle (in sq. units) is

For $a, b, h > 0$,if the slope of one of the lines represented by $a^2 x^2 + 2hxy + b^2 y^2 = 0$ is twice that of the other,then the value of $\frac{h}{ab}$ is

If the equation $hxy + gx + fy + c = 0$ represents a pair of straight lines,then

$A$ pair of straight lines drawn through the origin forms an isosceles triangle right-angled at the origin with the line $2x + 3y = 6$. The area (in sq. units) of the triangle so formed is

Vedclass Test Series

Exam Paper Generator

Online Exam Module