If ax2 + 4xy + y2 + ax + 3y + 2 = 0 represents a parabola, then a is

Question

If ax2 + 4xy + y2 + ax + 3y + 2 = 0 represents a parabola, then a is (A) -4 (B) 4 (C) 0 (D) 6

Tardigrade Admin · Accepted Answer

Given, ax2+4xy+y2+ax+3y+2=0 Since, the given equation represent a parabola, then it satisfies, H2=AB dots(i) On comparing with, Ax2+2Hxy+By2+2gx+2fy+c=0 Then, A=a, B=1 and H=2 From Eq. (i), (2)2=(a) (1), a=4

Q. If $a x^{2} + 4 x y + y^{2} + a x + 3 y + 2 = 0$ represents a parabola, then $a$ is

-4

4

0

6

Given, $a x^{2} + 4 x y + y^{2} + a x + 3 y + 2 = 0$
Since, the given equation represent a parabola, then it satisfies, $H^{2} = A B \dots (i)$
On comparing with,
$A x^{2} + 2 H x y + B y^{2} + 2 gx + 2 f y + c = 0$
Then, $A = a, B = 1$
and $H = 2$
From Eq. (i), $(2)^{2} = (a) (1)$ ,
$a = 4$

Q. If ax2+4xy+y2+ax+3y+2=0 represents a parabola, then a is

-4

4

0

6

Given, ax2+4xy+y2+ax+3y+2=0 Since, the given equation represent a parabola, then it satisfies, H2=AB…(i) On comparing with, Ax2+2Hxy+By2+2gx+2fy+c=0 Then, A=a,B=1 and H=2 From Eq. (i), (2)2=(a)(1), a=4

Q. If $a x^{2} + 4 x y + y^{2} + a x + 3 y + 2 = 0$ represents a parabola, then $a$ is

Given, $a x^{2} + 4 x y + y^{2} + a x + 3 y + 2 = 0$
Since, the given equation represent a parabola, then it satisfies, $H^{2} = A B \dots (i)$
On comparing with,
$A x^{2} + 2 H x y + B y^{2} + 2 gx + 2 f y + c = 0$
Then, $A = a, B = 1$
and $H = 2$
From Eq. (i), $(2)^{2} = (a) (1)$ ,
$a = 4$