Constructing a Line Tangent to a Circle
Constructing a line tangent to a circle is a fundamental geometric problem with practical applications in various fields such as engineering, physics, and computer graphics. This mathematical concept involves creating a straight line that touches a circle at a single point, creating a right angle with the circle's radius at that point. The process requires a precise understanding of geometric principles, specifically the properties of circles and angles. Mastering the construction of tangents is essential for solving problems related to curves and circles, making it a crucial skill in both theoretical and applied mathematics.
Questions
- The tangent and the normal to the conic #x^2/a^2+y^2/b^2=1# at a point #(acostheta, bsintheta)# meet the major axis in the points #P# and #P'#, where #PP'=a# Show that #e^2cos^2theta + costheta -1 = 0#, where #e# is the eccentricity of the conic?
- What is the circle with center (5, -6) tangent to the y axis?
- Find the equation of normal and tangent to the circle #x^2+y^2=4# at the point #(2cos45^@,2sin45^@)#?
- How do we find equation of tangent and normal to a circle at a given point?
- If two circles intersect at n points, then which of the following is true ? a) #n^2##<=#9, b) #n^3##<=#17, c) 2n + 3 #<=#4, d) n - 3 = 1
- Line CD is tangent to circle A at point B. segment AB is a radius of circle A. what can be concluded about angle ABD?
- The equation of tangent to the circle x^2+y^2=r^2 is y=mx+c ,then the point of contact of the circle and the tangent is?
- The tangents drawn from the origin to the circle #x^2 + y^2 -2rx -2hy +h^2=0# are perpendicular if?
- How length of /AC/ = ?
- What is the maximum possible distance between two points #R# and #T# on a circle, whose radius is #2# units?
- How can we bend a wire so as to maximize the area?
- I need help on which construction is illustrated in the attachment below ?
- How to show that the line 3x+4y=20 is a tangent to the circle x^2+y^2=16?
- Which statement about line BC is correct?
- Consider the circle #x^2+y^2-2x-14y+25=0#. For what values of m is the line y=mx tangent to this circle?
- How will you know if a center of a circle is tangent to y axis? Thank you so much for those will answer.
- Show that the surface of a sphere can't be represented as a plane (?)
- Can somebody explain this definition? **The radian is the plane between two radii of a circle which cut off on the circumference an arc, equal in length to the radius**
- Prove that the radius of the circle with equation x² + y² = 25 is perpendicular on the tangent line in P(3,4) to the circle? Thank you!
- Prove that the radius of the circle with equation x² + y² = 25 is perpendicular on the tangent line in P(3,4) to the circle? Thank you!