# JEE Main & Advanced Mathematics Straight Line Question Bank

### done Foot of perpendicular, Transformation, Pedal points Image of a point

• A) $\left( \frac{37}{10},-\frac{1}{10} \right)$

B) $\left( -\frac{1}{10},\frac{37}{10} \right)$

C) $\left( \frac{10}{37},-10 \right)$

D) $\left( \frac{2}{3},-\frac{1}{3} \right)$

• A) $\left( \frac{a}{2},\frac{b}{2} \right)$

B) $\left[ \frac{a}{2}(\cos \alpha +\cos \beta ),\frac{a}{2}(\sin \alpha +\sin \beta ) \right]$

C) $\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)$

D) None of these

• A) $\left( \frac{{{b}^{2}}{{x}_{1}}-ab{{y}_{1}}-ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}-ab{{x}_{1}}-bc}{{{a}^{2}}+{{b}^{2}}} \right)$

B) $\left( \frac{{{b}^{2}}{{x}_{1}}+ab{{y}_{1}}+ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}+ab{{x}_{1}}+bc}{{{a}^{2}}+{{b}^{2}}} \right)$

C) $\left( \frac{a{{x}_{1}}+b{{y}_{1}}+ab}{a+b},\frac{a{{x}_{1}}-b{{y}_{1}}-ab}{a+b} \right)$

D) None of these

• A) $\left( \frac{1}{3},\frac{3}{2} \right)$

B) $\left( -\frac{1}{2},\frac{3}{2} \right)$

C) $\left( \frac{4}{3},\frac{1}{2} \right)$

D) $\left( \frac{3}{4},\,\,-\frac{1}{2} \right)$

• A) $(-6,\,5)$

B) $(5,\,6)$

C) $(-5,\,6)$

D) $(6,\,5)$

• A) $23$ sq. units

B) $\frac{23}{2}sq.$units

C) $\frac{23}{3}sq.$units

D) None of these

• A) 18 sq. units

B) $18\sqrt{2}sq.$units

C) 18/$\sqrt{2}$sq. units

D) None of these

• A) $(-1,-1)$

B) $(2,2)$

C) $(-2,-2)$

D) None of these

• A) (4, 3)

B) (3, 4)

C) (1, 4)

D) $\left( \frac{7}{2},\frac{7}{2} \right)$

• A) ${{a}^{2}}+{{b}^{2}}={{p}^{2}}+{{q}^{2}}$

B) $\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}+\frac{1}{{{q}^{2}}}$

C) ${{a}^{2}}+{{p}^{2}}={{b}^{2}}+{{q}^{2}}$

D) $\frac{1}{{{a}^{2}}}+\frac{1}{{{p}^{2}}}=\frac{1}{{{b}^{2}}}+\frac{1}{{{q}^{2}}}$

• A) $\sqrt{2}$and 1

B) 1 and $\sqrt{2}$

C) $2\sqrt{2}$and $2\sqrt{2}/3$

D) $2\sqrt{2}/3$and $2\sqrt{2}$

• A) $\left( \frac{3}{5},2 \right)$

B) $\left( \frac{3}{5},\frac{4}{5} \right)$

C) $\left( -\frac{3}{5},-\frac{4}{5} \right)$

D) $\left( \frac{30}{17},\frac{19}{17} \right)$

• A) $(-1,-4)$

B) $(-3\,,\,\,-8)$

C) $(1,-4)$

D) $(3,\,8)$

• A) $(-1,-14)$

B) (3 ,4)

C) (1, 2)

D) (- 4, 13)

• A) 3x ? 2y + 5

B) 3x ? 2y + 10

C) 2x + 3y ? 5

D) 6x ? 4y ? 7

• A) ${{x}^{2}}+{{y}^{2}}-hx-ky=0$

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

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

D) None of these

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