What is the foci y=5x^2-12x+7 ?

The foci y=5x^2-12x+7 is (6/5 ,-3/20)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

foci y=5x^2-12x+7

foci

y = 5 x^{2} - 12 x + 7

(\frac{6}{5}, - \frac{3}{20})

Solution steps

Rewrite

y = 5 x^{2} - 12 x + 7

in the standard form

4 \cdot \frac{1}{20} (y - (- \frac{1}{5})) = (x - \frac{6}{5})^{2}

(h, k) = (\frac{6}{5}, - \frac{1}{5}), p = \frac{1}{20}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(\frac{6}{5}, - \frac{1}{5})

along the y-axis

(\frac{6}{5}, - \frac{1}{5} + p)

= (\frac{6}{5}, - \frac{1}{5} + \frac{1}{20})

Refine

(\frac{6}{5}, - \frac{3}{20})

4 x = y^{2} - 4 y

3 x^{2} - 12 x + 2 y + 15 = 0

y^{2} - 3 y

y^{2} - y - 42

3 x^{2} - 3 x