Two common tangents to the circle x^{2}+y^{2}=2a^{2}  and parabola y^{2}=8ax\; are

  • Option 1)

    x=\pm (y+2a)

  • Option 2)

    y=\pm (x+2a)

  • Option 3)

    x=\pm (y+a)

  • Option 4)

    y=\pm (x+a)

 

Answers (1)
S Sabhrant Ambastha

As we learnt in 

Equation of tangent -

y= mx+\frac{a}{m}

- wherein

Tengent to y^{2}=4ax is slope form.

 

 and

 

 

Condition of tangency -

c^{2}=a^{2}\; (1+m^{2})

 

- wherein

If  y=mx+c  is a tangent to the circle x^{2}+y^{2}=a^{2}

 

 

Tangent to circle x2+y2=2a2

is \: y=mx+\sqrt{2}a\sqrt{\left 1+m^{2} \right }

and Tangent to parabola y2=8ax

is \: y=mx+\frac{2a}{m}

we \: get \: \sqrt{2a} \: \sqrt{1+m^{2}}= \frac{2a}{m}

\\ (m^{2}+1)\cdot m^{2}=2 \\ \\ m^{4}+2m^{2}-m^{2}-2=0 \\ \\ m^{2}=1 \: \: \ ; \: \: \: m= \pm 1 \\ \\ we \: get \: \: \: y=\pm (x+2a)

 


Option 1)

x=\pm (y+2a)

This option is incorrect

Option 2)

y=\pm (x+2a)

This option is correct

Option 3)

x=\pm (y+a)

This option is incorrect

Option 4)

y=\pm (x+a)

This option is incorrect

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