The family of conics represented by the solution of differential equation (4x+3y+1) dx +(3x+2y+1)dy=0 is (a) circles (b) parabolas (c) hyperbolas (d) ellipses Which one of the following does not satisfy the differential equation d³y dx³ -y=0? 3 (a) ex (b) ex (c) e (d) e √(√x X sin COS √√3 2 X

Q: 15. x2 – 8x + 2y + 10 = 0 Equation:

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Q: 6. Find the equations of the asymptotes for the conic 25x²-150x-16y²-64y-239=0

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Q: 8. Find the equation of the conic whose focus is (4, -5) and directrix is x = -2.

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Q: x² = 1 = 1 II 4. 4, +

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Q: determine the equation  of the conic of foci (1,-2) and (5,-2), and eccentricity e=2/3

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Q: 19. Which equation's graph is a hyperbola? (A) x² + 16y2 = 144 (B) : x + 16y = 14- %3D (C) x2 – 16y2…

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Q: Direction: without transforming each general equation into the Standard form, identify the of conics…

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Q: 11x2-7y2-66x-28y-6=0 standard form of hyperbola

A: Given    standard form of Hyperbola

Q: 2. Identify the conic section given by y² + 2y = 4x² + 3 Find its vertex/vertices and focus/foci.

A: We rewrite the equation as: This is an equation of a hyperbola.

Q: 16x^2-9y^2+96x+18y-9=0 -conic? -equation of this conic in the form we used for graphing?

A: Explained below

Q: Which is the equation of an ellipse with direcrices at x = =-4 and foci at (2,0) and (-2,0)

A: Center is the midpoint of the foci  midpoint of (2,0) and (-2,0) is : Directrix = -4