Maths-
General
Easy
Question
Angle between tangents drawn from (1, 4) to parabola y2 = 4x is
/2
/3
/6
/4
The correct answer is:
/3
To find angle between tangents.
The equation of the tangent is y = mx + 1/m.
It passes through the point (1, 4).
![m squared minus 4 m plus 1 equals 0](data:image/png;base64,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)
m1 + m2 = 4, m1m2 = 1
|m1 – m2| = 2![square root of 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAATCAYAAACORR0GAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAR5JREFUeNpjYCAe8ADxfwow0SACiPcz0AFsB+IUWlsiAsTvoTRNQQYQr8ci7gjE24D4GxD/AOJbQDwBiIXJtQgUNyE4xIOAmA1JzACId5BjiQIQvwZiDhL0fCLHogognk2CeiUgvkGOReeB2IMIdeJAnAiNJy9CGRId6ADxcyBmwaMPPWMW4FKoAsTzoYps0OTagbifSJ8LAnEAEJ8EYntsCmqgFoHyySk0uftAbEJiUPNALcMJsoD4HzSsQcACiG8TCDZc4AchBaCMtwzKngzEDWRYogdNEHjBHCD+DvUFKO9oEFB/EIhDoeqZoCUFKLjjCVkkAMR/gXgtEB8nwvW2QLwFGlQ/oCWFD7FeP0womVILmEItkqFH3RNCbQMBMLZHLDCj6IAAAABYdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zcXJ0Pjxtbj4zPC9tbj48L21zcXJ0PjwvbWF0aD6vi/NRAAAAAElFTkSuQmCC)
tan θ = 2
/ 2 = ![square root of 3](data:image/png;base64,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)
θ =
/3
Therefore, the angle between tangents is /3
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In the adjoining figure along which axis the moment of inertia of the triangular lamina will be maximum- [Given that ![A B less than B C less than A C right square bracket](data:image/png;base64,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)
![](data:image/png;base64,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)
In the adjoining figure along which axis the moment of inertia of the triangular lamina will be maximum- [Given that ![A B less than B C less than A C right square bracket](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
Three particles, each of mass m are situated at the vertices of an equilateral triangle ABC of side
cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram
units will be :
![](data:image/png;base64,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)
Three particles, each of mass m are situated at the vertices of an equilateral triangle ABC of side
cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram
units will be :
![](data:image/png;base64,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)
physics-General
Maths-
The locus of the middle points of chords of a parabola which subtend a right angle at the vertex of the parabola is
The locus of the middle points of chords of a parabola which subtend a right angle at the vertex of the parabola is
Maths-General
maths-
If the parabola y2 = 4ax passes through (3, 2), then length of latus rectum of the parabola is
If the parabola y2 = 4ax passes through (3, 2), then length of latus rectum of the parabola is
maths-General
maths-
The locus of the poles of focal chord of the parabola y2 = 4ax is
The locus of the poles of focal chord of the parabola y2 = 4ax is
maths-General
maths-
The locus of the mid points of the chords of the parabola y2 = 4ax which passes through a given point (β,
)
The locus of the mid points of the chords of the parabola y2 = 4ax which passes through a given point (β,
)
maths-General
maths-
The equation of common tangent to the curves y2 = 8x and xy = –1 is
The equation of common tangent to the curves y2 = 8x and xy = –1 is
maths-General
maths-
Angle between tangents drawn from the point (1, 4) to the parabola y2 = 4x is
Angle between tangents drawn from the point (1, 4) to the parabola y2 = 4x is
maths-General
maths-
The general equation of 2nd degree 9x2 –24xy + 16y2 – 20x –15y – 60 = 0 represents
The general equation of 2nd degree 9x2 –24xy + 16y2 – 20x –15y – 60 = 0 represents
maths-General
maths-
If (2, 0) is the vertex and y-axis is the directrix of the parabola then its focus is
If (2, 0) is the vertex and y-axis is the directrix of the parabola then its focus is
maths-General
maths-
The equation of directrix of the parabola y2 + 4y + 4x + 2 = 0 is
The equation of directrix of the parabola y2 + 4y + 4x + 2 = 0 is
maths-General