Locus of the point dividing the join of a fixed point and a point moving on a conic

1. A.
   $x = a$
2. B.
   $x = 0$
3. C.
   $x = - \frac{a}{2}$
4. D.
   $x = \frac{a}{2}$

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1. A.
   $9x^{2} + 4y^{2} + 18x + 8y + 145 = 0$
2. B.
   $36x^{2} + 16y^{2} + 90x + 56y + 145 = 0$
3. C.
   $36x^{2} + 16y^{2} + 108x + 80y + 145 = 0$
4. D.
   $36x^{2} + 16y^{2} + 72x + 32y + 145 = 0$

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1. A.
   $\frac{1}{4}$
2. B.
   $\frac{1}{2}$
3. C.
   1
4. D.
   $\frac{1}{3}$

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1. A.
   $\frac{\sqrt{3}}{2}$
2. B.
   $\frac{1}{2\sqrt{2}}$
3. C.
   $\frac{1}{\sqrt{2}}$
4. D.
   $\frac{1}{2}$

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1. A.
   $\frac{6\sqrt{5}}{5}$
2. B.
   $\frac{4\sqrt{5}}{5}$
3. C.
   $\frac{2\sqrt{5}}{5}$
4. D.
   $\frac{3\sqrt{5}}{5}$

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