The lesson is analytic geometry standartize the conic (7x2+4xy+4y2−2x−6y+1=0

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The lesson is analytic geometry standartize the conic  (7x2+4xy+4y2−2x−6y+1=0

Papilys3q · Accepted Answer

Step 1Comparing the equation with standard formax2+2hxy+by2+2gx+2fy+c=0⇒a=7, h=2, b=4, g=−1, f=−3, c=1△=abc+2fgh−af2−bg2−ch2△=28+2(−3)(−1)(2)−7(−3)2−4(−1)2−1(2)2△=40−63−4−2≠0Nowh2−ab=(2)2−7×4−24&amp;lt;0and a≠bSo, curve represents an Elipse1) 7x2+4xy+4y2−2x−6y+1=0Now find the angle by which the axes are rotatedSo, cot⁡2θ=a−b2hcot⁡2θ=7−44=34So, cos⁡2θ=35Step 2Now, sin⁡θ=1−cos⁡2θ2=15So, cos⁡θ=1+cos⁡2θ2=25Substitute sin⁡θ of cos⁡θ in rotation formulaex=x′cos⁡θ−y′sin⁡θ and y=x′sin⁡θ+y′cos⁡θx=2x′−y′5 of y=x′+2y′5Substituting x of y in eqn (1)7(2x′−y′5)2+4(2x′−y′)(x;+2y′)5+4(x′+2y′5

autormtak0w · Accepted Answer

Step 1  Given, y=6x+1, point (x1y1)=(−7,1)  We know that,  Step 2  y=6x+1  If is in the form of y=mx+c  Slope m=6  Point (x1y1)=(−7,1)  equation of a line parallel to y=6x+1  y−y1=m(x−x1)  y−1=6(x−(−7))  y−1=6(x+7)  y−1=6x+42  y=6x+42+1  y=6x+43

The lesson is analytic geometry standartize the conic (7x^{2}+4xy+4y^{2}-2x-6y+1=0

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