James is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 16 inches × 14 1/4 inch
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Answer:
Step-by-step explanation:
we want to figure out the ellipse equation which passes through <u>(</u><u>1</u><u>,</u><u>4</u><u>)</u><u> </u>and <u>(</u><u>-</u><u>3</u><u>,</u><u>2</u><u>)</u>
the standard form of ellipse equation is given by:
where:
- (h,k) is the centre
- a is the horizontal redius
- b is the vertical radius
since the centre of the equation is not mentioned, we'd assume it (0,0) therefore our equation will be:
substituting the value of x and y from the point (1,4),we'd acquire:
similarly using the point (-3,2), we'd obtain:
let 1/a² and 1/b² be q and p respectively and transform the equation:
solving the system of linear equation will yield:
substitute back:
divide both equation by 1 which yields:
substitute the value of a² and b² in the ellipse equation , thus:
simplify complex fraction:
and we're done!
(refer the attachment as well)
