How to draw graph of $r = 3 sin θ + 4 cos θ$ $r= 3sintheta+4costheta$ ?

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Answer 1 · 2018-03-12T08:58:41

Draw a circle with a center at $(2, \frac{3}{2})$ $(2,3/2)$ with a radius of $2.5$ $2.5$ .

Multiply both sides by $r$ $r$ to get $r^{2} = 3 r sin θ + 4 r cos θ$ $r^2=3rsintheta+4rcostheta$

$r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$
$3 r sin θ = 3 y$ $3rsintheta=3y$
$4 r cos θ = 4 x$ $4rcostheta=4x$

$x^{2} + y^{2} = 3 y + 4 x$ $x^2+y^2=3y+4x$

$x^{2} - 4 x + y^{2} - 3 y = 0$ $x^2-4x+y^2-3y=0$

${(x - 2)}^{2} - 4 + {(y - \frac{3}{2})}^{2} - \frac{9}{4} = 0$ $(x-2)^2-4+(y-3/2)^2-9/4=0$

${(x - 2)}^{2} + {(y - \frac{3}{2})}^{2} = 4 + \frac{9}{4} = \frac{25}{4}$ $(x-2)^2+(y-3/2)^2=4+9/4=25/4$

Draw a circle with a center at $(2, \frac{3}{2})$ $(2,3/2)$ with a radius of $2.5$ $2.5$ .

How to draw graph of r=3sinθ+4cosθr= 3sintheta+4costheta?