Question

4x^2-4xy+y^2-6=0,whether it's any conic(circle,ellipse,parabola or hyperbola) or not?explain a bit???

Answer 1

hi sirm

Answer 2

If x² and y² both have the same coefficients like x² + y² or 3x² + 3y², then it is a circle.

If x² and y² both have different coefficients that have the same sign, like 4x² + 9y², or x² + 16y², then it is an ellipse.

If x² and y² have different signs, like 25x² - 9y², or 16y² - x², then it is a hyperbola.

If the equation has either x² and y², but not both, then it is a parabola.
i'm not getting yet(:

Answer 3

the general form of a conic section is \[\large Ax^2+Bxy+Cy^2+Dx+Ey+F=0\] the discriminant \[\large B^2-4AC\] can identify the conic section according to this rule:

parabola (or denegerate) when \[B^2-4AC=0\]
ellipse (or degenerate) when \[B^2-4AC<0\] and hyperbola (or degenerate) when \[B^2-4AC > 0\]

Answer 4

i have to find diccrimant frist to know whether this is conic or not?

Answer 5

yes.

Answer 6

okay but the equation i wrote i think it's not conicor it is?

Answer 7

can you identify A, B and C in the equation above?

Answer 8

sure

Answer 9

A=4,B=-4 and C=1

Answer 10

what is the value of the discriminant \[B^2 - 4AC\] is it positive (hyperbola), negative(ellipse), or zero (parabola)?

Answer 11

it's zero is it?

Answer 12

parabola that is

Answer 13

thank u so much

Answer 14

one question more?\[Y ^{2=4\sqrt{2}}X\]

Answer 15

how we find discrimant of this type of equation?

Answer 16

?

Answer 17

is this the equation? \[\large y^2=4\sqrt{2}x\]

Answer 18

no actually the question is\[x^{2}-2xy+y ^{2}-8x-8y=0\]

Answer 19

''by a rotation of axes,eliminate the xyterm and identify the conic and find its elements?

Answer 20

i have notes in which this question is solved and there is wriiten like this\[Y ^{2}=4\sqrt{2}\]

Answer 21

which represent parabola

Answer 22

so it is a parabola with line of symmetry the Y-axis

Answer 23

how we come to know it is parabola?

Answer 24

without discriminant how u know?

Answer 25

the discriminant should be applied when there is an Bxy term, otherwise use the forms of the conic sections
parabola: 4a(y-h)=(x-h)^2 or 4a(x-h)=(y-k)^2
ellipse: (x-h)^2/a^2 + (y-k)^2/b^2 = 1
hyperbola: (x-h)^2/a^2 - (y-k)^2/b^2 = 1

Answer 26

in standard form (unrotated axis), a parabola has only one squared variable. in an ellipse or hyperbola, both variables are squared. it is an ellipse if the coefficients of x^2 and y^2 have the same sign, hyperbola if they have opposite signs (assuming that both terms are on the same side of the equation of the conic).

Answer 27

yeah

Answer 28

thanks again