-is-most-appropriate-when-sketching-a-circle-given-in-standard-form-x-h2-y-k2-r2

Question

Which first action is most appropriate when sketching a circle given in standard form (x−h)2+(y−k)2=r2\left(x-h\$$right)^2$$+\left(y-k\$$right)^2$$=$$r^2$$?

Accepted Answer

Plot the center point (h,k)\left(h,k\right) and mark rr units up, down, left, and right before drawing the smooth circle.

Answer

First, expand both squared binomials to obtain the $$x2x^2$$ and $$y2y^2$$ terms. Then, draw the curve by approximating the level sets of the quadratic form.

Answer

Set y=0y=0 and solve for xx to find the x-intercepts, then use those points to help determine the shape of the entire circle.

Answer

Compute the derivative  ⁣dy ⁣dx\!\frac{\mathrm{dy}}{\!\mathrm{d}x} and sketch tangent lines at several points to outline the circle.

Which first action is most appropriate when sketching a circle given in standard form (x−h)2+(y−k)2=r2\(\left\)(x-h\(\right\))^2+\(\left\)(y-k\(\right\))^2=r^2?

Which first action is most appropriate when sketching a circle given in standard form ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ ?