# JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank

### done Transformation of axes and Locus

• A) (5, 3)

B) (3, 5)

C) (3, 7)

D) None of these

• A) (3, 2)

B) (- 3, 2)

C) (2, - 3)

D) None of these

• A) ${{y}^{2}}-2ax={{a}^{2}}$

B) ${{y}^{2}}-2ax+{{a}^{2}}=0$

C) ${{y}^{2}}+2ax+{{a}^{2}}=0$

D) ${{y}^{2}}+2ax={{a}^{2}}$

• A) $12{{x}^{2}}+4{{y}^{2}}=3$

B) $12{{x}^{2}}-4{{y}^{2}}=3$

C) $12{{x}^{2}}-4{{y}^{2}}+3=0$

D) $12{{x}^{2}}+4{{y}^{2}}+3=0$

• A) $x-\sqrt{3}y=0$

B) $x+\sqrt{3}y=0$

C) $\sqrt{3}x+y=0$

D) $\sqrt{3}x-y=0$

• A) A straight line

B) A circle

C) A parabola

D) An ellipse

• A) A straight line parallel to x-axis

B) A circle through origin

C) A circle with centre at the origin

D) A straight line parallel to y-axis

• A) $(x-3y)(x+3y)=0$

B) $(x-3y)(x+y)=0$

C) $(3x-y)(3x+y)=0$

D) None of these

• A) ${{x}^{2}}+{{y}^{2}}-2=0$

B) ${{x}^{2}}+{{y}^{2}}+2=0$

C) ${{x}^{2}}+{{y}^{2}}+4=0$

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

• A) ${{y}^{2}}=4ax$

B) ${{x}^{2}}=4ay$

C) ${{y}^{2}}+4ax=0$

D) ${{x}^{2}}+4ay=0$

• A) ${{x}^{2}}+3{{y}^{2}}=0$

B) ${{x}^{2}}-3{{y}^{2}}=0$

C) $3{{x}^{2}}+{{y}^{2}}=0$

D) $3{{x}^{2}}-{{y}^{2}}=0$

• A) A line

B) A circle

C) A parabola

D) An ellipse

• A) $x=2y$

B) $y=2x$

C) $x=5y+1$

D) $y=2x+3$

• A) $4x-3y=0$

B) $4x+3y=0$

C) $3x+4y=0$

D) $3x-4y=0$

• A) A circle

B) Perpendicular bisector of the line segment AB

C) A line parallel to x-axis

D) None of these

• A) $2ax-{{k}^{2}}=0$

B) $2ax+{{k}^{2}}=0$

C) $2ay-{{k}^{2}}=0$

D) $2ay+{{k}^{2}}=0$

• A) A straight line

B) A circle

C) An ellipse

D) A hyperbola

• A) ${{k}^{2}}({{x}^{2}}+{{y}^{2}})-{{a}^{2}}=0$

B) ${{x}^{2}}+{{y}^{2}}-{{k}^{2}}{{a}^{2}}=0$

C) ${{x}^{2}}+{{y}^{2}}+{{a}^{2}}=0$

D) ${{x}^{2}}+{{y}^{2}}-{{a}^{2}}=0$

• A) ${{x}^{2}}-8{{y}^{2}}=0$

B) ${{x}^{2}}+8{{y}^{2}}=0$

C) $4{{x}^{2}}-{{y}^{2}}=0$

D) ${{x}^{2}}-4{{y}^{2}}=0$

• A) ${{x}^{2}}+8x+4y-20=0$

B) ${{x}^{2}}-8x-4y+20=0$

C) ${{y}^{2}}-4y-8x+20=0$

D) None of these

• A) ${{x}^{2}}+{{y}^{2}}=4{{p}^{2}}$

B) $\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=\frac{4}{{{p}^{2}}}$

C) ${{x}^{2}}+{{y}^{2}}=\frac{4}{{{p}^{2}}}$

D) $\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=\frac{2}{{{p}^{2}}}$

• A) ${{x}^{2}}+{{y}^{2}}+2gx+2fy+k=0$

B) ${{x}^{2}}-{{y}^{2}}+2gx+2fy+k=0$

C) ${{x}^{2}}+{{y}^{2}}+2xy+2gx+2fy+k=0$

D) None of these

• A) $5{{x}^{2}}-5{{y}^{2}}-72x+54y+225=0$

B) $5{{x}^{2}}-5{{y}^{2}}+72x+54y+225=0$

C) $5{{x}^{2}}+5{{y}^{2}}+72x+54y+225=0$

D) $5{{x}^{2}}+5{{y}^{2}}-72x+54y+225=0$

• A) $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$

B) $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$

C) $\frac{{{x}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}+\frac{{{y}^{2}}}{{{a}^{2}}}=1$

D) None of these

• A) $3{{x}^{2}}+{{y}^{2}}+26x+44y-131=0$

B) ${{x}^{2}}+3{{y}^{2}}-26x+44y-131=0$

C) $3({{x}^{2}}+{{y}^{2}})+26x-44y+131=0$

D) None of these

• A) ${{x}^{2}}+{{y}^{2}}=4$

B) ${{x}^{2}}+{{y}^{2}}=16$

C) ${{x}^{2}}+{{y}^{2}}=2$

D) None of these

• A) ${{x}^{2}}+{{y}^{2}}=2{{a}^{2}}$

B) ${{x}^{2}}-{{y}^{2}}={{a}^{2}}$

C) ${{x}^{2}}+{{y}^{2}}+{{a}^{2}}=0$

D) ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$

• A) Parabola

B) Ellipse

C) Hyperbola

D) None of these

• A) Hyperbola

B) Circle

C) Parabola

D) Ellipse

• A) Hyperbola

B) Circle

C) Parabola

D) Ellipse

• A) $(x+3y-1)(x+3y-23)=0$

B) $(x+3y+1)(x+3y-23)=0$

C) $(3x+y-1)(3x+y-23)=0$

D) $(3x+y+1)(3x+y+23)=0$

• A) A circle

B) A parabola

C) An ellipse

D) None of these

• A) ${{x}^{2}}+{{y}^{2}}-2x-4y+1=0$

B) $3({{x}^{2}}+{{y}^{2}})-2x-4y+1=0$

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

D) None of these

• A) $a_{1}^{2}-a_{2}^{2}+b_{1}^{2}-b_{2}^{2}$

B) $\sqrt{a_{1}^{2}+b_{1}^{2}-a_{2}^{2}-b_{2}^{2}}$

C) $\frac{1}{2}(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2})$

D) $\frac{1}{2}(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2})$

• A) ${{x}^{2}}-12y=36$

B) ${{y}^{2}}+12x=36$

C) ${{y}^{2}}-12x=36$

D) ${{x}^{2}}+12y=36$

• A) $\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{5}=1$

B) $\frac{{{x}^{2}}}{5}-\frac{{{y}^{2}}}{4}=1$

C) $\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{3}=1$

D) $\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1$

• A) ${{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}$

B) ${{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}$

C) ${{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}$

D) ${{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}$

• A) $x-y=0$

B) $ax+by=0$

C) $bx-ay=0$

D) $x+y=0$

• A) ${{x}^{2}}+{{y}^{2}}-4y=0$

B) ${{x}^{2}}+{{y}^{2}}-4|y|=0$

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

D) ${{x}^{2}}+{{y}^{2}}-4|x|=0$

• A) ${{x}^{2}}+4y+2=0$
B) ${{x}^{2}}-4y+2=0$
C) ${{y}^{2}}-4x+2=0$
D) ${{y}^{2}}+4x+2=0$