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Find the maximum area of the ellipse (x^...

Find the maximum area of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` which touches the line `y=3x+2.`

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A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which has O A=a ,O B=b . Then find the area between the arc A B and the chord A B of the ellipse.

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If the chords of contact of tangents from two poinst (x_1, y_1) and (x_2, y_2) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are at right angles, then find the value of (x_1x_2)/(y_1y_2)dot

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