Two Tangents Meeting at a Known Angle
Difficulty: Medium · Topics: Geometry, Conic Sections, Ellipse
Ma’lum burchak ostida kesishuvchi ikki urinma
From the point A(0, 5) on the circle x^2+y^2=25, two tangent lines are drawn to the ellipse dfracx^2a^2+dfracy^24=1, and the acute angle between them is θ.
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If tanθ=3/4, find the value of 3a^2. (Here 0<a<2.)
x^2+y^2=25 aylanadagi A(0, 5) nuqtadan dfracx^2a^2+dfracy^24=1 ellipsga ikkita urinma o‘tkazilgan, ular orasidagi o‘tkir burchak θ.
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Agar tanθ=3/4 bo‘lsa, 3a^2 ning qiymatini toping. (Bu yerda 0<a<2.)