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Acute angle between the lines represented by a second-degree equation

This type of question, asked 5 times: 13 Apr 2026 S2, 15 Apr 2026 S1, 16 Apr 2026 S2, 17 Apr 2026 S1, 15 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    13 Apr 2026 S2

    58
    The pair of straight lines represented by the equation 3x2−4xy+3y2=0\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0 are

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  2. Question 2

    15 Apr 2026 S1

    57
    If θ\theta is the acute angle between the lines represented by the equation x2−3xy+2y2=0x^2 - 3xy + 2y^2 = 0, then 3sin⁡θ+2cos⁡θ3sin⁡θ−2cos⁡θ=\dfrac{3\sin\theta + 2\cos\theta}{3\sin\theta - 2\cos\theta} =

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  3. Question 3

    16 Apr 2026 S2

    56
    If θ\theta is the acute angle between the lines 2x2+7xy+3y2=02x^2 + 7xy + 3y^2 = 0, then the value of 2cos⁡θ−3sin⁡θ4sin⁡θ+5cos⁡θ=…\dfrac{2\cos\theta - 3\sin\theta}{4\sin\theta + 5\cos\theta} = \ldots

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  4. Question 4

    17 Apr 2026 S1

    56
    The measure of the acute angle between the pair of lines 2x2+xy−y2−x+2y−1=02x^2 + xy - y^2 - x + 2y - 1 = 0 is:

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  5. Question 5

    15 May 2026 S2

    58
    If θ1\theta_1 and θ2\theta_2 are the acute angles between the lines 3x2−7xy+4y2=03x^2 - 7xy + 4y^2 = 0 and 6x2−5xy+y2=06x^2 - 5xy + y^2 = 0 respectively, then ...

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