120637 If \(x \cos \alpha+y \sin \alpha=P\) is a tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then

120638 The product of the perpendiculars from the foci on any tangent of the ellipse \(5 x^2+8 y^2=40\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Hence, [UPSEE-2015], \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), On comparing standard ellipse equation, \(a^2=18, \quad b^2=32\), Since the major axis is along the y-axis, \(\therefore \quad\) Equation of tangent, \(x=m y+\sqrt{a^2 m^2+b^2}\), \(x=m y+\sqrt{18 m^2+32}\), Slope of tangent \(=\frac{1}{\mathrm{~m}}=-\frac{4}{3}\), \(m=-\frac{3}{4}\), equation of tangent is \(4 x+3 y=24\), \(\frac{4 x}{24}+\frac{3 y}{24}=\frac{24}{24}\), \(\frac{x}{6}+\frac{y}{8}=1\), The line intersect coordinate axis at \(\mathrm{A}(0,8), \mathrm{B}(6,0)\), and \(\mathrm{C}(0,0)\), \(\text { Area of } \triangle \mathrm{AOB} =\frac{1}{2} \times 6 \times 8\), \(=24 \text { sq. unit }\), 901. The equations of the tangents drawn at the ends of the major axis of the ellipse \(9 x^2+5 y^2-\) \(30 \mathrm{y}=0\) are,

120639 The equation of tangents to the ellipse \(3 x^2+4 y^2\) \(=5\), which are inclined at \(30^{\circ}\) to the \(\mathrm{X}\)-axis, are
#[Qdiff: Hard, QCat: Numerical Based, examname: JCECE-2014], \(\frac{\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\), On comparing standard ellipse equation,

120640 If any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) intercepts equal lengths ' \(l\) ' on the axes, then \(l\) is equal to

120641 If \(m\) is the slope of a common tangent to the curves \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and \(x^2+y^2=12\), then \(12 m^2\) is equal to :

120637 If \(x \cos \alpha+y \sin \alpha=P\) is a tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then

120638 The product of the perpendiculars from the foci on any tangent of the ellipse \(5 x^2+8 y^2=40\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Hence, [UPSEE-2015], \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), On comparing standard ellipse equation, \(a^2=18, \quad b^2=32\), Since the major axis is along the y-axis, \(\therefore \quad\) Equation of tangent, \(x=m y+\sqrt{a^2 m^2+b^2}\), \(x=m y+\sqrt{18 m^2+32}\), Slope of tangent \(=\frac{1}{\mathrm{~m}}=-\frac{4}{3}\), \(m=-\frac{3}{4}\), equation of tangent is \(4 x+3 y=24\), \(\frac{4 x}{24}+\frac{3 y}{24}=\frac{24}{24}\), \(\frac{x}{6}+\frac{y}{8}=1\), The line intersect coordinate axis at \(\mathrm{A}(0,8), \mathrm{B}(6,0)\), and \(\mathrm{C}(0,0)\), \(\text { Area of } \triangle \mathrm{AOB} =\frac{1}{2} \times 6 \times 8\), \(=24 \text { sq. unit }\), 901. The equations of the tangents drawn at the ends of the major axis of the ellipse \(9 x^2+5 y^2-\) \(30 \mathrm{y}=0\) are,

120639 The equation of tangents to the ellipse \(3 x^2+4 y^2\) \(=5\), which are inclined at \(30^{\circ}\) to the \(\mathrm{X}\)-axis, are
#[Qdiff: Hard, QCat: Numerical Based, examname: JCECE-2014], \(\frac{\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\), On comparing standard ellipse equation,

120640 If any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) intercepts equal lengths ' \(l\) ' on the axes, then \(l\) is equal to

120641 If \(m\) is the slope of a common tangent to the curves \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and \(x^2+y^2=12\), then \(12 m^2\) is equal to :

120637 If \(x \cos \alpha+y \sin \alpha=P\) is a tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then

120638 The product of the perpendiculars from the foci on any tangent of the ellipse \(5 x^2+8 y^2=40\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Hence, [UPSEE-2015], \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), On comparing standard ellipse equation, \(a^2=18, \quad b^2=32\), Since the major axis is along the y-axis, \(\therefore \quad\) Equation of tangent, \(x=m y+\sqrt{a^2 m^2+b^2}\), \(x=m y+\sqrt{18 m^2+32}\), Slope of tangent \(=\frac{1}{\mathrm{~m}}=-\frac{4}{3}\), \(m=-\frac{3}{4}\), equation of tangent is \(4 x+3 y=24\), \(\frac{4 x}{24}+\frac{3 y}{24}=\frac{24}{24}\), \(\frac{x}{6}+\frac{y}{8}=1\), The line intersect coordinate axis at \(\mathrm{A}(0,8), \mathrm{B}(6,0)\), and \(\mathrm{C}(0,0)\), \(\text { Area of } \triangle \mathrm{AOB} =\frac{1}{2} \times 6 \times 8\), \(=24 \text { sq. unit }\), 901. The equations of the tangents drawn at the ends of the major axis of the ellipse \(9 x^2+5 y^2-\) \(30 \mathrm{y}=0\) are,

120639 The equation of tangents to the ellipse \(3 x^2+4 y^2\) \(=5\), which are inclined at \(30^{\circ}\) to the \(\mathrm{X}\)-axis, are
#[Qdiff: Hard, QCat: Numerical Based, examname: JCECE-2014], \(\frac{\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\), On comparing standard ellipse equation,

120640 If any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) intercepts equal lengths ' \(l\) ' on the axes, then \(l\) is equal to

120641 If \(m\) is the slope of a common tangent to the curves \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and \(x^2+y^2=12\), then \(12 m^2\) is equal to :

120637 If \(x \cos \alpha+y \sin \alpha=P\) is a tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then

120638 The product of the perpendiculars from the foci on any tangent of the ellipse \(5 x^2+8 y^2=40\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Hence, [UPSEE-2015], \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), On comparing standard ellipse equation, \(a^2=18, \quad b^2=32\), Since the major axis is along the y-axis, \(\therefore \quad\) Equation of tangent, \(x=m y+\sqrt{a^2 m^2+b^2}\), \(x=m y+\sqrt{18 m^2+32}\), Slope of tangent \(=\frac{1}{\mathrm{~m}}=-\frac{4}{3}\), \(m=-\frac{3}{4}\), equation of tangent is \(4 x+3 y=24\), \(\frac{4 x}{24}+\frac{3 y}{24}=\frac{24}{24}\), \(\frac{x}{6}+\frac{y}{8}=1\), The line intersect coordinate axis at \(\mathrm{A}(0,8), \mathrm{B}(6,0)\), and \(\mathrm{C}(0,0)\), \(\text { Area of } \triangle \mathrm{AOB} =\frac{1}{2} \times 6 \times 8\), \(=24 \text { sq. unit }\), 901. The equations of the tangents drawn at the ends of the major axis of the ellipse \(9 x^2+5 y^2-\) \(30 \mathrm{y}=0\) are,

120639 The equation of tangents to the ellipse \(3 x^2+4 y^2\) \(=5\), which are inclined at \(30^{\circ}\) to the \(\mathrm{X}\)-axis, are
#[Qdiff: Hard, QCat: Numerical Based, examname: JCECE-2014], \(\frac{\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\), On comparing standard ellipse equation,

120640 If any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) intercepts equal lengths ' \(l\) ' on the axes, then \(l\) is equal to

120641 If \(m\) is the slope of a common tangent to the curves \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and \(x^2+y^2=12\), then \(12 m^2\) is equal to :

120637 If \(x \cos \alpha+y \sin \alpha=P\) is a tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then

120638 The product of the perpendiculars from the foci on any tangent of the ellipse \(5 x^2+8 y^2=40\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Hence, [UPSEE-2015], \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), On comparing standard ellipse equation, \(a^2=18, \quad b^2=32\), Since the major axis is along the y-axis, \(\therefore \quad\) Equation of tangent, \(x=m y+\sqrt{a^2 m^2+b^2}\), \(x=m y+\sqrt{18 m^2+32}\), Slope of tangent \(=\frac{1}{\mathrm{~m}}=-\frac{4}{3}\), \(m=-\frac{3}{4}\), equation of tangent is \(4 x+3 y=24\), \(\frac{4 x}{24}+\frac{3 y}{24}=\frac{24}{24}\), \(\frac{x}{6}+\frac{y}{8}=1\), The line intersect coordinate axis at \(\mathrm{A}(0,8), \mathrm{B}(6,0)\), and \(\mathrm{C}(0,0)\), \(\text { Area of } \triangle \mathrm{AOB} =\frac{1}{2} \times 6 \times 8\), \(=24 \text { sq. unit }\), 901. The equations of the tangents drawn at the ends of the major axis of the ellipse \(9 x^2+5 y^2-\) \(30 \mathrm{y}=0\) are,

120639 The equation of tangents to the ellipse \(3 x^2+4 y^2\) \(=5\), which are inclined at \(30^{\circ}\) to the \(\mathrm{X}\)-axis, are
#[Qdiff: Hard, QCat: Numerical Based, examname: JCECE-2014], \(\frac{\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\), On comparing standard ellipse equation,

120640 If any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) intercepts equal lengths ' \(l\) ' on the axes, then \(l\) is equal to

120641 If \(m\) is the slope of a common tangent to the curves \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and \(x^2+y^2=12\), then \(12 m^2\) is equal to :