## Condition for Line Tangent to the Ellipse

The condition for a line $$y = mx + c$$ to be the tangent to the ellipse $$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}… Click here to read more

From basic to higher mathematics

The condition for a line $$y = mx + c$$ to be the tangent to the ellipse $$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}… Click here to read more

The equations of tangent and normal to the ellipse $$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$$ at the point $$\left( {{x_1},{y_1}} \right)$$… Click here to read more

Find the equation of the tangent and normal to the ellipse $$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$$ at the point $$\left(… Click here to read more

Example 1: An arch is in the form of a semi-ellipse, and it is $$48$$ feet wide at the base… Click here to read more

A hyperbola is the set of all points in the plane, the difference of whose distance from two fixed distinct… Click here to read more

The midpoint of the line segment joining the foci is called the centre of the hyperbola. In the given diagram… Click here to read more

There are two types of hyperbolas: one hyperbola’s conjugate axis is $$X$$-axis and the other’s conjugate axis is $$Y$$-axis. In the… Click here to read more

To prove the equation of a hyperbola, let $$P\left( {x,y} \right)$$ be any point of the hyperbola and $$M\left( {\frac{a}{e},y}… Click here to read more

Example: Find an equation of the hyperbola with centre at origin, focus at $$\left( {7,0} \right)$$ and vertex at the… Click here to read more

In conic section geometry, a straight line is known as the tangent to a hyperbola. If this straight line meets… Click here to read more

A line $$y = mx + c$$ intersects a hyperbola $$\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$$ at two points maximum and the condition… Click here to read more

The line $$y = mx + c$$ does not intersect the hyperbola $$\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$$, so the condition… Click here to read more

The condition for a line $$y = mx + c$$ to be the tangent to the hyperbola $$\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}}… Click here to read more

The equations of the tangent and normal to the hyperbola $$\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$$ at the point $$\left( {{x_1},{y_1}}… Click here to read more

Show that the $$\left( {a\sec \theta ,b\tan \theta } \right)$$ always lies on the hyperbola $$\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$$…. Click here to read more

General Equation of the Second Degree: The equation of the form \[a{x^2} + b{y^2} + 2hxy + 2gx + 2fy… Click here to read more

The equation of the tangent to the conic $$a{x^2} + b{y^2} + 2hxy + 2gx + 2fy + c =… Click here to read more

It is known from algebra that the simultaneous solution set of two equations of the second degree consists of four… Click here to read more

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