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

The equation $x^3 + 8y^3 + 24xy = 64$ represents:

The equation of the lines passing through the origin and having slopes $3$ and $-\frac{1}{3}$ is

One of the lines represented by the equation ${x^2} + 6xy = 0$ is

If the sum and product of the slopes of the lines represented by $4x^2 + 2hxy - 7y^2 = 0$ are equal,then $h = \dots$

If the equation $ax^{2} + hxy + by^{2} = 0$ represents a pair of coincident lines,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module