UGC NET CSE | November 2017 | Part 3 | Question: 16

Question

Find the equation of the circle $x^2+y^2=1$ in terms of $x’y’$ coordinates, assuming that the $xy$ coordinate system results from a scaling of $3$ units in the $x’$ direction and $4$ units in the $y’$ direction.

• A. $3(x’)^2+4(y’)^2=1$
• B. $\bigg( \dfrac{x’}{3} \bigg) ^2 + \bigg( \dfrac{y’}{4} \bigg) ^2 =1$
• C. $(3x’)^2+ (4y’)^2=1$
• D. $\dfrac{1}{3}(x’)^2 + \dfrac{1}{4}(y’)^2=1$

Comments

Nothing is seen!

Answer 1

Scaling a Curve

Let f[x,y]==0 be the equation for a curve in rectangular coordinates. To scale the curve by s, the new equation would be: f[x/s, y/s]==0

Let f[θ,r]==0 be the equation for a curve in polar coordinate. To scale it by s, the new formula is f[r/s,θ]==0.

Replace x to x'/3 and y to y'/4,so answer will be option (2).

see this http://xahlee.info/SpecialPlaneCurves_dir/CoordinateSystem_dir/transformation.html