If $P$ is a point equidistant from all the vertices $A(-1,3), B(3,5), C(5,7)$ of a $\triangle A B C$, then $P A=$

4 different pairs of lines are given in List I and the cosine of the angle between every pair of lines is given in List II. Match the following :

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>7</mn>

<mi>y</mi>

<mn>2</mn>

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>7</mn>

<mi>y</mi>

<mn>2</mn>

<msqrt>

  <mn>3</mn>

</msqrt>

<mn>2</mn>

<msqrt>

  <mn>3</mn>

</msqrt>

<mn>2</mn>

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>11</mn>

<mi>y</mi>

<mn>2</mn>

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>11</mn>

<mi>y</mi>

<mn>2</mn>

<mo data-mjx-texclass="OPEN">(</mo>

<mfrac>

  <mn>1</mn>

  <mrow>

    <mn>2</mn>

    <msqrt>

      <mn>3</mn>

    </msqrt>

  </mrow>

</mfrac>

<mo data-mjx-texclass="CLOSE">)</mo>

<mrow>

  <mfrac>

    <mn>1</mn>

    <mrow>

      <mn>2</mn>

      <msqrt>

        <mn>3</mn>

      </msqrt>

    </mrow>

  </mfrac>  

</mrow>  

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>2</mn>

<mi>y</mi>

<mn>2</mn>

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>2</mn>

<mi>y</mi>

<mn>2</mn>

<mn>1</mn>

<mn>2</mn>

<mn>1</mn>

<mn>2</mn>

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>2</mn>

<mi>y</mi>

<mn>2</mn>

<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>

<mn>2</mn>

<mi>y</mi>

<mn>2</mn>

<mo data-mjx-texclass="OPEN">(</mo>

<mfrac>

  <mn>2</mn>

  <mn>3</mn>

</mfrac>

<mo data-mjx-texclass="CLOSE">)</mo>

<mrow>

  <mfrac>

    <mn>2</mn>

    <mn>3</mn>

  </mfrac>  

</mrow>  

<mn>1</mn>

<msqrt>

  <mn>2</mn>

</msqrt>

<mn>1</mn>

<msqrt>

  <mn>2</mn>

</msqrt>

If $a x^2+6 x y-2 y^2=0$ represents a pair of perpendicular lines and $9 x^2+2 h x y+4 y^2=0(h>0)$ represents a pair of coincident lines, then $h=$

The line $x+2 y=k$ meets the curve $2 x^2-2 x y+3 y^2+2 x-y-1=0$ at two points $A$ and $B$. Let $O$ be the origin. If the line segments $O A$ and $O B$ are perpendicular to each other, then $k=$