88386 If the lines \(3 x+y-4=0, x-a y-10=0, b x+2 y\) \(+9=0\) form three successive sides of a rectangle in an order and the fourth side passes through \((1,2)\), then the area of that rectangle (in sq. units) is

88387 The points \(A(2,1), B(3,-2)\) and \(C(a, b)\) are vertices of the rectangle \(A B C D\). If the point \(P\) \((3,4)\) lies on \(\mathrm{CD}\) produced, then \(5 \mathrm{a}+10 \mathrm{~b}=\)

88388 Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(\mathbf{a}^{2}+11 a+\) \(3\left(\mathbf{m}_{2}^{2}+\mathbf{m}_{2}^{2}\right)=220\). If one vertex of the square a
is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), where \(\alpha \in\left(0, \frac{\pi}{2}\right)\) and the equation of one diagonal is \((\cos \alpha-\sin \alpha) \mathrm{x}+(\sin \alpha+\cos \alpha) \mathrm{y}=10\), then 72 \(\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+\mathbf{a}^{2}-3 a+13\) is equal to:

88380 If \(h^{2}=a b\), then the slopes of the lines represented by \(a x^{2}-2 h x y+b y^{2}=0\) would be in the ratio

88386 If the lines \(3 x+y-4=0, x-a y-10=0, b x+2 y\) \(+9=0\) form three successive sides of a rectangle in an order and the fourth side passes through \((1,2)\), then the area of that rectangle (in sq. units) is

88387 The points \(A(2,1), B(3,-2)\) and \(C(a, b)\) are vertices of the rectangle \(A B C D\). If the point \(P\) \((3,4)\) lies on \(\mathrm{CD}\) produced, then \(5 \mathrm{a}+10 \mathrm{~b}=\)

88388 Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(\mathbf{a}^{2}+11 a+\) \(3\left(\mathbf{m}_{2}^{2}+\mathbf{m}_{2}^{2}\right)=220\). If one vertex of the square a
is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), where \(\alpha \in\left(0, \frac{\pi}{2}\right)\) and the equation of one diagonal is \((\cos \alpha-\sin \alpha) \mathrm{x}+(\sin \alpha+\cos \alpha) \mathrm{y}=10\), then 72 \(\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+\mathbf{a}^{2}-3 a+13\) is equal to:

88380 If \(h^{2}=a b\), then the slopes of the lines represented by \(a x^{2}-2 h x y+b y^{2}=0\) would be in the ratio

88386 If the lines \(3 x+y-4=0, x-a y-10=0, b x+2 y\) \(+9=0\) form three successive sides of a rectangle in an order and the fourth side passes through \((1,2)\), then the area of that rectangle (in sq. units) is

88387 The points \(A(2,1), B(3,-2)\) and \(C(a, b)\) are vertices of the rectangle \(A B C D\). If the point \(P\) \((3,4)\) lies on \(\mathrm{CD}\) produced, then \(5 \mathrm{a}+10 \mathrm{~b}=\)

88388 Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(\mathbf{a}^{2}+11 a+\) \(3\left(\mathbf{m}_{2}^{2}+\mathbf{m}_{2}^{2}\right)=220\). If one vertex of the square a
is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), where \(\alpha \in\left(0, \frac{\pi}{2}\right)\) and the equation of one diagonal is \((\cos \alpha-\sin \alpha) \mathrm{x}+(\sin \alpha+\cos \alpha) \mathrm{y}=10\), then 72 \(\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+\mathbf{a}^{2}-3 a+13\) is equal to:

88380 If \(h^{2}=a b\), then the slopes of the lines represented by \(a x^{2}-2 h x y+b y^{2}=0\) would be in the ratio

88386 If the lines \(3 x+y-4=0, x-a y-10=0, b x+2 y\) \(+9=0\) form three successive sides of a rectangle in an order and the fourth side passes through \((1,2)\), then the area of that rectangle (in sq. units) is

88387 The points \(A(2,1), B(3,-2)\) and \(C(a, b)\) are vertices of the rectangle \(A B C D\). If the point \(P\) \((3,4)\) lies on \(\mathrm{CD}\) produced, then \(5 \mathrm{a}+10 \mathrm{~b}=\)

88388 Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(\mathbf{a}^{2}+11 a+\) \(3\left(\mathbf{m}_{2}^{2}+\mathbf{m}_{2}^{2}\right)=220\). If one vertex of the square a
is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), where \(\alpha \in\left(0, \frac{\pi}{2}\right)\) and the equation of one diagonal is \((\cos \alpha-\sin \alpha) \mathrm{x}+(\sin \alpha+\cos \alpha) \mathrm{y}=10\), then 72 \(\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+\mathbf{a}^{2}-3 a+13\) is equal to:

88380 If \(h^{2}=a b\), then the slopes of the lines represented by \(a x^{2}-2 h x y+b y^{2}=0\) would be in the ratio