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Sagot :
Given:
The conic equation is:
[tex]2x^2+Cy^2+3x+5y+1=0[/tex]
To find:
The value of C such that the given conic equation make a parabola.
Solution:
The general for of conic equation is:
[tex]Ax^2+Cy^2+Dx+Ey+F=0[/tex]
This equation represents a parabola is either A=0 or C=0 but not both equal to zero.
The given equation is:
[tex]2x^2+Cy^2+3x+5y+1=0[/tex]
Here, coefficient of [tex]x^2[/tex] is A=2 and coefficient of [tec]y^2[/tex] is C.
Since A is not equal to 0, therefore C must be equal to 0 to form a parabola.
Therefore, the only value of C is 0.
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