What is 3x+5y=5x^2+1 ?

The solution to 3x+5y=5x^2+1 is Parabola with (h,k)=(3/10 , 11/100),p= 1/4

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3x+5y=5x^2+1

3 x + 5 y = 5 x^{2} + 1

(h, k) = (\frac{3}{10}, \frac{11}{100}), p = \frac{1}{4}

Solution steps

3 x + 5 y = 5 x^{2} + 1

Rewrite

3 x + 5 y = 5 x^{2} + 1

in the standard form

4 \cdot \frac{1}{4} (y - \frac{11}{100}) = (x - \frac{3}{10})^{2}

Therefore parabola properties are:

(h, k) = (\frac{3}{10}, \frac{11}{100}), p = \frac{1}{4}

y^{2} = 3 x + 1

(y - 8)^{2} = - 4 (x - 3)

4 x + y^{2} - 6 y + 1 = 0

5 x^{2} + y = 13

\frac{k ( x )}{x + 2} \geq \frac{x ^{2}}{x + 2}

What is 3x+5y=5x^2+1 ?
The solution to 3x+5y=5x^2+1 is Parabola with (h,k)=(3/10 , 11/100),p= 1/4