What is (6p+5q)2=36p^2+25q^2 ?

The solution to (6p+5q)2=36p^2+25q^2 is Ellipse with (h,k)=(1/6 , 1/5),a= 1/(3sqrt(2)),b=(sqrt(2))/5

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(6p+5q)2=36p^2+25q^2

(6 p + 5 q) 2 = 36 p^{2} + 25 q^{2}

(h, k) = (\frac{1}{6}, \frac{1}{5}), a = \frac{1}{3 2}, b = \frac{2}{5}

Solution steps

(6 p + 5 q) \cdot 2 = 36 p^{2} + 25 q^{2}

Rewrite

(6 p + 5 q) 2 - 36 p^{2} - 25 q^{2} = 0

in the form of the standard ellipse equation

\frac{( p - \frac{1}{6} ) ^{2}}{( \frac{1}{3 2} ) ^{2}} + \frac{( q - \frac{1}{5} ) ^{2}}{( \frac{2}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{6}, \frac{1}{5}), a = \frac{1}{3 2}, b = \frac{2}{5}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{6}, \frac{1}{5}), b = \frac{2}{5}, a = \frac{1}{3 2}

3 x^{2} + 54 x + 243 + 2 y^{2} - 6 = 0

4 x^{2} + 9 y^{2} - 24 x + 36 y - 72 = 0

0.04 = 0.01 x^{2} + 0.04 y^{2}

3 x^{2} + 2 y^{2} \geq 18

144 y^{2} + 169 x^{2} = 169 \cdot 144

What is (6p+5q)2=36p^2+25q^2 ?
The solution to (6p+5q)2=36p^2+25q^2 is Ellipse with (h,k)=(1/6 , 1/5),a= 1/(3sqrt(2)),b=(sqrt(2))/5